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# Pk nag engineering thermodynamics solutions pdf

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Thermodynamics Contents Chapter Introduction Chapter Temperature Chapter Work and Heat Transfer Chapter First Law of Thermodynamics Chapter

If a refrigerator is used for heating purposes in winter so that the atmosphere becomes the cold body and the room to be heated becomes the hot body, how much heat would be available for heating for each kW input to the driving motor?

How does this compare with resistance heating? COP ref. If this system is used as a heat pump, how many MJ of heat would be available for heating for each MJ of heat input to the engine?

Q COP H. An electric storage battery which can exchange heat only with a constant temperature atmosphere goes through a complete cycle of two processes. In process 12, 2. During process 21, 2. What is the maximum possible work? Heat flow out to the atmosphere.

As Electric energy stored in a battery is High grade energy so it can be completely converted to the work. A household refrigerator is maintained at a temperature of 2C. Every time the door is opened, warm material is placed inside, introducing an average of kJ, but making only a small change in the temperature of the refrigerator. The cost of work is Rs.

What is the monthly bill for this refrigerator? The atmosphere is at 30C. A heat pump working on the Carnot cycle takes in heat from a reservoir at 5C and delivers heat to a reservoir at 60C. The heat pump is driven by a reversible heat engine which takes in heat from a reservoir at C and rejects heat to a reservoir at 60C.

## p k nag solution

The reversible heat engine also drives a machine that absorbs 30 kW. A refrigeration plant for a food store operates as a reversed Carnot heat engine cycle. The store is to be maintained at a temperature of 5C and the heat transfer from the store to the cycle is at the rate of 5 kW. If heat is transferred from the cycle to the atmosphere at a temperature of 25C, calculate the power required to drive the plant.

A heat engine is used to drive a heat pump. The heat transfers from the heat engine and from the heat pump are used to heat the water circulating through the radiators of a building. Evaluate the ratio of the heat transfer to the circulating water to the heat transfer to the heat engine. Engine A receives kJ at a temperature of C from a hot source, while engine B is in communication with a cold sink at a temperature of 4.

If the work output of A is twice that of B, find a The intermediate temperature between A and B b The efficiency of each engine c The heat rejected to the cold sink Ans. It drives a heat pump which uses river water at 4.

Assuming that a temperature difference of Why is direct heating thermodynamically more wasteful? An ice-making plant produces ice at atmospheric pressure and at 0C from water.

The mean temperature of the cooling water circulating through the condenser of the refrigerating machine is 18C. Evaluate the minimum electrical work in kWh required to produce 1 tonne of ice The enthalpy of fusion of ice at atmospheric pressure is A reversible engine works between three thermal reservoirs, A, B and C.

The engine absorbs an equal amount of heat from the thermal reservoirs A and B kept at temperatures TA and TB respectively, and rejects heat to the thermal reservoir C kept at temperature TC. The efficiency of the engine is times the efficiency of the reversible engine, which works between the two reservoirs A and C.

The energy rejected from this engine is received by a second reversible engine at the same temperature T. Show that: Two Carnot engines A and B are connected in series between two thermal reservoirs maintained at K and K respectively. Engine A receives kJ of heat from the high-temperature reservoir and rejects heat to the Carnot engine B. Engine B takes in heat rejected by engine A and rejects heat to the low-temperature reservoir.

If engines A and B have equal thermal efficiencies, determine a The heat rejected by engine B b The temperature at which heat is rejected by engine, A c The work done during the process by engines, A and B respectively. Q2 A heat pump is to be used to heat a house in winter and then reversed to cool the house in summer. The interior temperature is to be maintained at 20C.

Heat transfer through the walls and roof is estimated to be 0. Consider an engine in outer space which operates on the Carnot cycle. The only way in which heat can be transferred from the engine is by radiation. The rate at which heat is radiated is proportional to the fourth power of the absolute temperature and to the area of the radiating surface. It takes 10 kW to keep the interior of a certain house at 20C when the outside temperature is 0C. This heat flow is usually obtained directly by burning gas or oil.

Calculate the power required if the 10 kW heat flow were supplied by operating a reversible engine with the house as the upper reservoir and the outside surroundings as the lower reservoir, so that the power were used only to perform work needed to operate the engine. Prove that the COP of a reversible refrigerator operating between two given temperatures is the maximum. Suppose A is any refrigerator and B is reversible refrigerator and also assume. But it violates the KelvinPlank statement i.

A house is to be maintained at a temperature of 20C by means of a heat pump pumping heat from the atmosphere. Heat losses through the walls of the house are estimated at 0. For the same room temperature, the same heat loss rate, and the same power input to the pump, what is the maximum permissible atmospheric temperature? The three heat transfer rates are Qh, Qa, and Qc respectively. If the collector captures 0. A heat engine operating between two reservoirs at K and K is used to drive a heat pump which extracts heat from the reservoir at K at a rate twice that at which the engine rejects heat to it.

What is the rate of heat rejection from the heat pump if the rate of heat supply to the engine is 50 kW? A reversible power cycle is used to drive a reversible heat pump cycle. The power cycle takes in Q1 heat units at T1 and rejects Q2 at T2. The heat pump abstracts Q4 from the sink at T4 and discharges Q3 at T3.

Q4 T4 T1 T2. Prove that the following propositions are logically equivalent: On the basis of the first law fill in the blank spaces in the following table of imaginary heat engine cycles. On the basis of the second law classify each cycle as reversible, irreversible, or impossible.

How much does the entropy of 1 kg of ice change as it melts into water in each of the following ways: Two kg of water at 80C are mixed adiabatically with 3 kg of water at 30C in a constant pressure process of 1 atmosphere. In a Carnot cycle, heat is supplied at C and rejected at 27C. The working fluid is water which, while receiving heat, evaporates from liquid at C to steam at C.

The associated entropy change is 1. There are no other heat transfers. Page 72 of Chapter 7 from these results show which case is irreversible, which reversible, and which impossible: The oval figure is a reversible cycle, where heat is absorbed at temperature less than, or equal to, T1, and rejected at temperatures greater than, or equal to, T2.

Prove that the efficiency of the oval cycle is less than that of the Carnot cycle. Water is heated at a constant pressure of 0. The boiling point is The initial temperature of water is 0C. The latent heat of evaporation is Find the increase of entropy of water, if the final state is steam Ans. One kg of air initially at 0. Process 1: Expansion followed by a constant volume heating. Determine the change of internal energy, enthalpy, and entropy for each process, and find the work transfer and heat transfer for each process.

Ten grammes of water at 20C is converted into ice at 10C at constant atmospheric pressure. Assuming the specific heat of liquid water to remain constant at 4.

Calculate the entropy change of the universe as a result of the following processes: A system maintained at constant volume is initially at temperature T1, and a heat reservoir at the lower temperature T0 is available.

Show that the maximum work recoverable as the system is cooled to T0 is. If the temperature of the atmosphere is 5C on a winter day and if 1 kg of water at 90C is available, how much work can be obtained. Take cv, of water as 4. Chapter 7 T1 to T2. The body is then brought back to its initial state by contact with a single reservoir at temperature T1.

Calculate the changes of entropy of the body and of the reservoirs. What is the total change in entropy of the whole system? If the initial heating were accomplished merely by bringing the body into contact with a single reservoir at T2, what would the various entropy changes be?

A body of finite mass is originally at temperature T1, which is higher than that of a reservoir at temperature T2. Suppose an engine operates in a cycle between the body and the reservoir until it lowers the temperature of the body from T1 to T2, thus extracting heat Q from the body.

If the engine does work W, then it will reject heat QW to the reservoir at T2. Their initial temperatures are K, K, and K. A heat reservoir at 0C and a reversible work source are available. What is the maximum amount of work that can be transferred to the reversible work source as the system is cooled from C to the temperature of the reservoir? If the bodies are initially at temperatures K and K and if a reversible work source is available, what are the maximum and minimum final common temperatures to which the two bodies can be brought?

What is the maximum amount of work that can be transferred to the reversible work source? Find the amount and direction of heat interaction with other reservoirs. A fluid for which R is a constant and equal to 0. In one of these pipes the pressure and temperature are 5 bar and K and in the other pipe the pressure and temperature are 1 bar and K respectively. Determine which pressure and temperature refer to the inlet pipe.

A is the inlet pipe. Two vessels, A and B, each of volume 3 m3 may be connected by a tube of negligible volume.

Vessel a contains air at 0. Find the change of entropy when A is connected to B by working from the first principles and assuming the. For air take the relations as given in Example 7. It is cooled reversibly by transferring heat to a completely reversible cyclic heat engine until the block reaches 20C. The 20C room air serves as a constant temperature sink for the engine. Compute i the change in entropy for the block,. Chapter 7 ii the change in entropy for the room air, iii the work done by the engine.

Two bodies of equal heat capacities C and temperatures T1 and T2 form an adiabatically closed system. What will the final temperature be if one lets this system come to equilibrium a freely? S univ. A resistor of 30 ohms is maintained at a constant temperature of 27C while a current of 10 amperes is allowed to flow for 1 sec. Determine the entropy change of the resistor and the universe. The specific heat of the resistor is 0. An adiabatic vessel contains 2 kg of water at 25C.

By paddle-wheel work transfer, the temperature of water is increased to 30C. If the specific heat of water is assumed constant at 4. A copper rod is of length 1 m and diameter 0. One end of the rod is at C, and the other at 0C.

Calculate the rate of heat transfer along the rod and the rate of entropy production due to irreversibility of this heat transfer. A body of constant heat capacity Cp and at a temperature Ti is put in contact with a reservoir at a higher temperature Tf. The pressure remains constant while the body comes to equilibrium with the reservoir. Show that the entropy change of the universe is equal to. Prove that entropy change is positive. Final temperature of the body will be Tf.

An insulated 0. An experimenter now places 0. The specific heat of copper is 0. Page 88 of Compute the entropy increase of the universe resulting from the process. Two blocks of metal, each having a mass of 10 kg and a specific heat of 0. A reversible refrigerator receives heat from one block and rejects heat to the other.

Calculate the work required to cause a temperature difference of C between the two blocks. A body of finite mass is originally at a temperature T1, which is higher than that of a heat reservoir at a temperature T2.

An engine operates in infinitesimal cycles between the body and the reservoir until it lowers the temperature of the body from T1 to T2. In this process there is a heat flow Q out of the body. Page 90 of A block of iron weighing kg and having a temperature of C is immersed in 50 kg of water at a temperature of 20C. What will be the change of entropy of the combined system of iron and water? Specific heats of iron and water are 0.

The specific heat of water is assumed constant at 4. A 50 ohm resistor carrying a constant current of 1 A is kept at a constant temperature of 27C by a stream of cooling water. In a time interval of 1s a What is the change in entropy of the resistor?

A lump of ice with a mass of 1. After some time has elapsed the resulting water attains the temperature of the environment, K. Calculate the entropy production associated with this process. The latent heat of fusion of ice is An ideal gas is compressed reversibly and adiabatically from state a to state b. It is then heated reversibly at constant volume to state c.

Heat is then rejected reversibly from the gas at constant volume till it returns to state a. Express Ta in terms of Tb and Tc. Liquid water of mass 10 kg and temperature 20C is mixed with 2 kg of ice at 5C till equilibrium is reached at 1 atm pressure. Find the entropy change of the system. A thermally insulated ohm resistor carries a current of 1 A for 1 s. The initial temperature of the resistor is 10C. Its mass is 5 g and its specific heat is 0. Given for copper: Availability function: Page 95 of Questions with Solution P.

Nag What is the maximum useful work which can be obtained when kJ are abstracted from a heat reservoir at K in an environment at K? Available work from that dQ is dW. The surroundings are at 30C. The temperature of the surroundings is 30C. A hot spring produces water at a temperature of 56C. The water flows into a large lake, with a mean temperature of 14C, at a rate of 0. What is the rate of working of an ideal heat engine which uses all the available energy?

Find the available and unavailable energies of the heat added. Eighty kg of water at C are mixed with 50 kg of water at 60C, while the temperature of the surroundings is 15C.

Determine the decrease in available energy due to mixing. A lead storage battery used in an automobile is able to deliver 5. This energy is available for starting the car. Let compressed air be considered for doing an equivalent amount of work in starting the car. The compressed air is to be stored at 7 MPa, 25C. What is the volume of the tank that would be required to let the compressed air have an availability of 5. Ice is to be made from water supplied at 15C by the process shown in Figure.

The final temperature of the ice is 10C, and the final temperature of the water that is used as cooling water in the condenser is 30C. Determine the minimum work required to produce kg of ice. A pressure vessel has a volume of 1 m3 and contains air at 1.

The air is cooled to 25C by heat transfer to the surroundings at 25C. Calculate the availability in the initial and final states and the irreversibility of this process. The inlet conditions are 1 bar and K and the exit conditions are 7 bar and K.

Compute the net rate of availability transfer and the irreversibility. Determine the second law and isentropic efficiencies of the turbine. Air enters an adiabatic compressor at atmospheric conditions of 1 bar, 15C and leaves at 5. The mass flow rate is 0. After leaving the compressor, the air is cooled to 40C in an after-cooler. Calculate a The power required to drive the compressor b The rate of irreversibility for the overall process compressor and cooler. In a rotary compressor, air enters at 1.

Calculate the irreversibility and the entropy production for unit mass flow rate. The atmosphere is at 1. Neglect the K. In a steam boiler, the hot gases from a fire transfer heat to water which vaporizes at a constant temperature of The latent heat of vaporization of steam at 3. If the steam generation rate is The water rises in temperature from to K, where the gas falls in temperature from K to K. The gases are cooled from to C, while water enters at 65C. The flow rates of the gas and water are 0.

The constant pressure specific heats for the gas and water are 1. Calculate the rate of exergy loss due to heat transfer. The exhaust from a gas turbine at 1.

The heat transfer from the gas heats an air flow at constant pressure, which enters the heat exchanger at K. The mass flow rate of air is twice that of the gas and the surroundings are at 1.

Take cp for exhaust gas as 1. Neglect heat transfer to the surroundings and the changes in kinetic and potential energy. An air preheater is used to heat up the air used for combustion by cooling the outgoing products of combustion from a furnace. What power would be developed by the heat engines? A mass of 2 kg of air in a vessel expands from 3 bar, 70C to 1 bar, 40C, while receiving 1. The environment is at 0. Calculate the maximum work and the work done on the atmosphere. Air enters the compressor of a gas turbine at 1 bar, 30C and leaves the compressor at 4 bar.

Calculate per kg of air a The work of compression b The reversible work of compression c The irreversibility. For air, use. A mass of 6. Heat is transferred to the air from a reservoir at C. Until the temperature of air rises to C. The environment is at kPa, 17C. Determine a The initial and final availability of air b The maximum useful work associated with the process.

The environment is at kPa, 7C. Calculate per kg of air a The actual amount of work required b The minimum work required c The irreversibility of the process Ans.

Calculate per kg of air a The maximum work output b The actual work output c The irreversibility Ans. Because of poor thermal insulation the brine temperature increases from K at the pipe inlet to K at the exit. Neglecting pressure losses, calculate the irreversibility rate or rate of energy degradation associated with the heat leakage. In an adiabatic throttling process, energy per unit mass of enthalpy remains the same. However, there is a loss of exergy.

An ideal gas flowing at the rate m is throttled from pressure p1 to pressure p2 when the environment is at temperature T0. What is the rate of exergy loss due to throttling? Page of Air at 5 bar and 20C flows into an evacuated tank until the pressure in the tank is 5 bar. Assume that the process is adiabatic and the temperature of the surroundings is 20C. A Carnot cycle engine receives and rejects heat with a 20C temperature differential between itself and the thermal energy reservoirs.

The expansion and compression processes have a pressure ratio of If there is no temperature differential between inlet and outlet then from Q1 heat input Carnot cycle produce work.

Energy is received by a solar collector at the rate of kW from a source temperature of K. If 60 kW of this energy is lost to the surroundings at steady state and if the user temperature remains constant at K, what are the first law and the second law efficiencies?

For flow of an ideal gas through an insulated pipeline, the pressure drops from bar to 95 bar. If the gas flows at the rate of 1. The cylinder of an internal combustion engine contains gases at C, 58 bar. Expansion takes place through a volume ratio of 9 according to pv1. The surroundings are at 20C, 1. Determine the loss of availability, the work transfer and the heat transfer per unit mass. The respective mass flow rates of oil and water are Page of Gain of availability 1.

The slope of an isobar on the h-s co-ordinates is equal to the absolute saturation temperature at that pressure. And for that isobars on Mollier diagram diverges from one another. Super heated vapour: When the temperature of the vapour is greater than the saturation temperature corresponding to the given pressure. Compressed liquid: When the temperature of the liquid is less than the saturation temperature at the given pressure, the liquid is called compressed liquid.

Complete the following table of properties for 1 kg of water liquid, vapour or mixture. Superheat 0C 0 0 0 0 Chapter 9 Evaluate the specific volume, temperature, dryness fraction, internal energy, enthalpy, and entropy of steam. Show the process on a sketch of the pv diagram, and evaluate the pressure, increase in enthalpy, increase in internal energy, increase in entropy of steam, and the heat transfer.

Evaluate also the pressure at which the steam becomes dry saturated. Ten kg of water at 45C is heated at a constant pressure of 10 bar until it becomes superheated vapour at C. Find the change in volume, enthalpy, internal energy and entropy. Water at 40C is continuously sprayed into a pipeline carrying 5 tonnes of steam at 5 bar, C per hour. A rigid vessel contains 1 kg of a mixture of saturated water and saturated steam at a pressure of 0.

When the mixture is heated, the state passes through the critical point. Determine a The volume of the vessel b The mass of liquid and of vapour in the vessel initially Page of Chapter 9 c The temperature of the mixture when the pressure has risen to 3 MPa d The heat transfer required to produce the final state c. It is a rigid vessel so if we a Heat this then the process will be constant volume heating.

As it passes through critical point then at 3 MPa i. A rigid closed tank of volume 3 m3 contains 5 kg of wet steam at a pressure of kPa. The tank is heated until the steam becomes dry saturated. Determine the final pressure and the heat transfer to the tank. Compute the shaft power assuming that the device is adiabatic but considering kinetic and potential energy changes. How much error would be made if these terms were neglected?

Calculate the diameters of the inlet and discharge tubes. A sample of steam from a boiler drum at 3 MPa is put through a throttling calorimeter in which the pressure and temperature are found to be 0.

Find the quality of the sample taken from the boiler. It is desired to measure the quality of wet steam at 0. The quality of steam is expected to be not more than 0.

Will the use of a separating calorimeter, ahead of the throttling calorimeter, serve the purpose, if at best 5 C degree of superheat is desirable at the end of throttling? What is the minimum dryness fraction required at the exit of the separating calorimeter to satisfy this condition?

After throttling if pressure is atm. The following observations were recorded in an experiment with a combined separating and throttling calorimeter: Pressure in the steam main15 bar Mass of water drained from the separator0.

Chapter 9 x 2 4. But at 1 bar minimum 5 super heat i. Steam from an engine exhaust at 1. The calorimeter has two 1 kW heaters and the flow is measured to be 3. Find the quality in the engine exhaust. For the same mass flow and pressures, what is the maximum moisture that can be determined if the outlet temperature is at least C? Steam expands isentropically in a nozzle from 1 MPa, C to 10 kPa. Find the velocity of steam at the exit from the nozzle, and the exit area of the nozzle.

Neglect the velocity of steam at the inlet to the nozzle. The exhaust steam from the nozzle flows into a condenser and flows out as saturated water. The cooling water enters the condenser at 25C and leaves at 35C.

Determine the mass flow rate of cooling water. The exponent n has the value 1. Find the final specific volume, the final temperature, and the heat transferred per kg of fluid. Evaluate the final temperature of the emerging stream, if there is no pressure drop due to the mixing process. What would be the rate of increase in the entropy of the universe? This stream with a negligible velocity now expands adiabatically in a nozzle to a pressure of 1 kPa.

Determine the exit velocity of the stream and the exit area of the nozzle. It is throttled to 5 bar before expanding in the engine to 0. Determine per kg of steam a The heat loss in the pipeline b The temperature drop in passing through the throttle valve c The work output of the engine d The entropy change due to throttling e The entropy change in passing through the engine.

From Steam Table 5 bar Tank A Figure has a volume of 0. The valve is then opened, and the tanks eventually come to the same pressure,. Which is found to be 4 bar. During this process, heat is transferred such that the steam remains at C. What is the volume of tank B? Calculate the amount of heat which enters or leaves 1 kg of steam initially at 0. Changes in K.

It flows into an evacuated rigid container from a large source c which is maintained at the initial condition of the steam. Then kJ of shaft work is transferred to the steam, so that its final condition is 1 MPa and C. A sample of wet steam from a steam main flows steadily through a partially open valve into a pipeline in which is fitted an electric coil. The valve and the pipeline are well insulated. The steam mass flow rate is 0. The main pressure is 4 bar, and the pressure and temperature of the steam downstream of the coil are 2 bar and C respectively.

Steam velocities may be assumed to be negligible. Pressure is maintained as here enthalpy is less so it is not possible in throttling calorimeter. Two insulated tanks, A and B, are connected by a valve. Tank A has a volume of 0. Tank B has a volume of 0.

The valve is then opened, and the two tanks come to a uniform state. If there is no heat transfer during the process, what is the final pressure? Compute the entropy change of the universe. Enthalpy h B Sp. The vessel is then heated until the water inside is saturated vapour. Considering the vessel and water together as a system, calculate the heat transfer during this process. The density of aluminum is 2. For Steam Table At 4.

The combined stream of steam is throttled to 5 bar and then expanded isentropically in a nozzle to 2 bar. Determine a The state of steam after mixing b The state of steam after throttling c The increase in entropy due to throttling d The velocity of steam at the exit from the nozzle e The exit area of the nozzle.

Steam of 65 bar, C leaves the boiler to enter a steam turbine fitted with a throttle governor. At a reduced load, as the governor takes action, the pressure of steam is reduced to 59 bar by throttling before it is admitted to the turbine.

Evaluate the availabilities of steam before and after the throttling process and the irreversibility due to it. A mass of wet steam at temperature C is expanded at constant quality 0. It is then heated at constant pressure to a degree of superheat of Find the enthalpy and entropy changes during expansion and during heating. Draw the Ts and hs diagrams. As p 0, or T , the real gas approaches the ideal gas behaviour. Virial Expansions: What is the mass of air contained in a room 6 m 9 m 4 m if the pressure is The usual cooking gas mostly methane cylinder is about 25 cm in diameter and 80 cm in height.

It is changed to 12 MPa at room temperature 27C. If the cylinder is to be protected against excessive pressure by means of a fusible plug, at what temperature should the plug melt to limit the maximum pressure to 15 MPa? In cooking gas main component is ethen and it filled in 18 bar pressure. At that pressure it is not a gas it is liquid form in atmospheric temperature so its weight is amount 14 kg. Find the molecular weight and the gas constant R of the gas.

From an experimental determination the specific heat ratio for acetylene C2H2 is found to 1. Find the two specific heats. A supply of natural gas is required on a site m above storage level. The gas at - C, 1. If the work transfer to the gas at the pump is 15 kW, find the heat transfer to the gas between the two points.

Neglect the change in K. A constant volume chamber of 0. Heat is transferred to the air until the temperature is C. Find the work done, the heat transferred, and the changes in internal energy, enthalpy and entropy. One kg of air in a closed system, initially at 5C and occupying 0.

There is no work other than pdv work. Find a the work done during the process, b the heat transferred, and c the entropy change of the gas. Air in a closed stationary system expands in a reversible adiabatic process from 0. Find the final temperature, and per kg of air, the change in enthalpy, the heat transferred, and the work done. If the above process occurs in an open steady flow system, find the final temperature, and per kg of air, the change in internal energy, the heat transferred, and the shaft work.

Neglect velocity and elevation changes. The indicator diagram for a certain water-cooled cylinder and piston air compressor shows that during compression pv1. The compression starts at kPa, 25C and ends at kPa. If the process is reversible, how much heat is transferred per kg of air? The gas is compressed according to the law pv1. Calculate the volume and temperature at the end of compression and heating, work done, heat transferred, and the total change of entropy.

Calculate the change of entropy when 1 kg of air changes from a temperature of K and a volume of 0. For the total path, find the work transfer, the heat transfer, and the change of entropy. An ideal gas cycle of three processes uses Argon Mol. Process is a reversible adiabatic expansion from 0. Process is a reversible isothermal process. Process is a constant pressure process in which heat transfer is zero. Sketch the cycle in the p-v and T-s planes, and find a the work transfer in process , b the work transfer in process , and c the net work of the cycle.

A gas occupies 0. It is expanded in the nonflow process according to the law pv1. Chapter 10 after which it is heated at constant pressure back to its original temperature. Sketch the process on the p-v and T-s diagrams, and calculate for the whole process the work done, the heat transferred, and the change of entropy.

It then expands in a cylinder poly tropically to its original temperature and the index of expansion is 1. Finally, it is compressed isothermally to its original volume. Calculate a the change of entropy during each of the three stages, b the pressures at the end of constant volume heat addition and at the end of expansion. Sketch the processes on the p-v and T-s diagrams. Try please. Find a the volume of the mixture, b the partial volumes of the components, c the partial pressures of the components, d the mole fractions of the components, e the specific heats cP and cV of the mixture, and f the gas constant of the mixture.

A gaseous mixture consists of 1 kg of oxygen and 2 kg of nitrogen at a pressure of kPa and a temperature of 20C.

Determine the changes in internal energy, enthalpy and entropy of the mixture when the mixture is heated to a temperature of C a at constant volume, and b at constant pressure. A closed rigid cylinder is divided by a diaphragm into two equal compartments, each of volume 0. Each compartment contains air at a temperature of 20C.

The pressure in one compartment is 2. The diaphragm is ruptured so that the air in both the compartments mixes to bring the pressure to a uniform value throughout the cylinder which is insulated. Find the net change of entropy for the mixing process. A vessel is divided into three compartments a , b , and c by two partitions. Part a contains oxygen and has a volume of 0. All three parts are at a pressure of 2 bar and a temperature of 13C.

When the partitions are removed and the gases mix, determine the change of entropy of each constituent, the final pressure in the vessel and the partial pressure of each gas. The vessel may be taken as being completely isolated from its surroundings.

A Carnot cycle uses 1 kg of air as the working fluid. The maximum and minimum temperatures of the cycle are K and K. The maximum pressure of the cycle is 1 MPa and the volume of the gas doubles during the isothermal heating process. Show by calculation of net work and heat supplied that the efficiency is the maximum possible for the given maximum and minimum temperatures. An ideal gas cycle consists of three reversible processes in the following sequence: Sketch the cycle on the p-v and T'-s diagrams. The number of moles, the pressures, and the temperatures of gases a, b, and c are given below Gas m kg mol P kPa t 0C N2 1 CO 3 O2 2 If the containers are connected, allowing the gases to mix freely, find a the pressure and temperature of the resulting mixture at equilibrium, and b the change of entropy of each constituent and that of the mixture.

Calculate the volume of 2. At this volume and the given pressure, what would the temperature be in K, if steam behaved like a van der Waals gas? The critical pressure, volume, and temperature of steam are Two vessels, A and B, each of volume 3 m 3 may be connected together by a tube of negligible volume.

Vessel a contains air at 7 bar, 95C while B Page of Find the change of entropy when A is connected to B. Assume the mixing to be complete and adiabatic. A valve is opened momentarily and the pressure falls immediately to 6.

Sometimes later the temperature is again 18C and the pressure is observed to be 9. Estimate the value of specific heat ratio. If intermediate temperature is T then p1 V1 pV 9.

Calculate the molecular weight of the mixture, the characteristic gas constant R for the mixture and the value of the reversible adiabatic index.

At 10C, the c p values of nitrogen, hydrogen, and carbon dioxide are l. A cylinder contains 0. The gas undergoes a reversible non-flow process during which its volume is reduced to one-fifth of its original value. If the law of compression is pv1. Heat flow through system] Page of Two moles of an ideal gas at temperature T and pressure p are contained in a compartment.

In an adjacent compartment is one mole of an ideal gas at temperature 2Tand pressure p. The gases mix adiabatically but do not react chemically when a partition separating: Show that the entropy increase due to the mixing process is given by 27 Provided that the gases are different and that the ratio of specific heat is the same for both gases and remains constant.

What would the entropy change be if the mixing gases were of the same Species? In an adjoining compartment, separated by a partition, are n2 moles of an ideal gas at pressure p2 and temperature T.

When the partition is removed, calculate a the final pressure of the mixture, b the entropy change when the gases are identical, and c the entropy change when. Prove that the entropy change in c is the same as that produced by two independent free expansions. Assume that 20 kg of steam are required at a pressure of bar and a temperature of C in order to conduct a particular experiment. A litre heavy duty tank is available for storage. Predict if this is an adequate storage capacity using: Estimate the error in each.

Estimate the pressure of 5 kg of CO2 gas which occupies a volume of 0. Compare this result with the value obtained using the generalized compressibility chart. Which is more accurate and why? Measurements of pressure and temperature at various stages in an adiabatic air turbine show that the states of air lie on the line pv1. Chapter 10 constant. A mass of an ideal gas exists initially at a pressure of kPa, temperature K, and specific volume 0.

The value of r is 1. Assuming air as an ideal gas, determine the work done and the heat transferred. Air contained in a cylinder fitted with a piston is compressed reversibly according to the law pv1.

The mass of air in the cylinder is 0. The initial pressure is kPa and the initial temperature 20C. Determine the work and the heat transfer. Air is contained in a cylinder fitted with a frictionless piston. Initially the cylinder contains 0. A closed system allows nitrogen to expand reversibly from a volume of 0. The original pressure of the gas is kPa and its initial temperature is C. Chapter 10 8. If the initial pressure of the gas is 1 atm, calculate the final pressure, the heat transfer, the work done and the change in entropy.

Determine the final pressure and the change of entropy per kg of air. In a heat engine cycle, air is isothermally compressed. Heat is then added at constant pressure, after Page which of the air expands isentropically to.

Chapter 10 its original state. Draw the cycle on p-v and T'-s coordinates. Determine the pressure ratio and the cycle efficiency if the initial temperature is 27C and the maximum temperature is C. Compartment 1 has a volume of 0. The partition is removed and the gases are allowed to mix. The mixture is now compressed reversibly and adiabatically to 1. Compute c the final temperature of the mixture, d The work required per unit mass, and e The specific entropy change for each gas.

Take c p of methane and. An ideal gas cycle consists of the following reversible processes: Show that the efficiency of this cycle is given by.

Where rk is the compression ratio and a is the ratio of pressures after and before heat addition. An engine operating on the above cycle with a compression ratio of 6 starts the compression with air at 1 bar, K.

If the ratio of pressures after and before heat addition is 2. Show that the ratio of the slope of the adiabatic curve to the slope of the isothermal curve is equal to. Both processes have a pressure ratio of 6. Two containers p and q with rigid walls contain two different monatomic gases with masses m p and m q , gas constants Rp and Rq , and initial temperatures Tp and Tq respectively, are brought in contact.

A system consisting of this gas confined by a cylinder and a piston undergoes a Carnot cycle between two pressures P1 and P2. The gravimetric analysis of dry air is approximately: Theorem 1. Where z, M and N are functions of x and y. Differentiating M partially with respect to y, and N with respect to x. This is the condition of exact or perfect differential. Theorem 2. If a quantity f is a function of x, y and z, and a relation exists among x, y and z, then f is a function of any two of x, y and z.

Similarly any one of x, y and z may be regarded to be a function of f and any one of x, y and z. Theorem 3. Among the variables x, y, and z any one variable may be considered as a function of the other two. Among the thermodynamic variables p, V and T. A pure substance existing in a single phase has only two independent variables. This is a very important equation in thermodynamics.

It indicates the following important facts. Cp Cv is always T p. T positive. Therefore, Cp is always greater than Cv.

Or specific volume T p minimum. Estimate the steam pressure in kPa.

## Solutions to Basic and Applied Thermodynamics PK NAG Solutions

Take the density of mercury as What is the absolute pressure in the condenser in kPa when the atmospheric pressure is Page 10 of Temperature By: S K Mondal Chapter 2 2. Nag The limiting value of the ratio of the pressure of gas at the steam point and at the triple point of water when the gas is kept at constant volume is found to be 1. What is the ideal gas temperature of the steam point? Water b. Sulphur b. Plot the ratio of Sb. This Page 11 of S K Mondal gives the ratio of Sb. On a gas thermometer operating at zero gas pressure, i.

What is the boiling point of sulphur on the gas scale, from your plot? Chapter 2 1. S K Mondal Q2. Suppose the e. Where a and b are constants. The values of K are found to be 1. Determine the temperature corresponding to a reading of K equal to 2. When operating at full load under steady state conditions, the motor is switched off and the resistance of the windings, immediately measured again, is found to be 93 ohms.

Find the temperature attained by the coil during full load. At what temperature both the Celsius and the new temperature scale reading would be the same?

## Solutions to Basic and Applied Thermodynamics PK NAG Solutions | Entropy | Temperature

The wire resistance was found to be 10 ohm and 16 ohm at ice point and steam point respectively, and 30 ohm at sulphur boiling point of Work and Heat Transfer By: S K Mondal 3. Nag Q3. Compute the work the pump must do upon the water in an hour just to force the water into the tank against the pressure. Sketch the system upon which the work is done before and after the process. The pressure in the cylinder is uniform during the process at 80 kPa, while the atmospheric pressure is Estimate the displacement work done by the air finally in the cylinder.

An engine cylinder has a piston of area 0. The gas expands according to a process which is represented by a straight line on a pressure-volume diagram. The final pressure is 0. Calculate the work done by the gas on the piston if the stroke is 0. A mass of 1. The initial density of air is 1. Find the work done by the piston to compress the air. A mass of gas is compressed in a quasi-static process from 80 kPa, 0. The indicator spring constant is MPa per m. The pump runs at 50 rpm. The pump cylinder diameter is 0.

Find the rate in kW at which the piston does work on the water. S K Mondal Q3. Chapter 3 A single-cylinder, single-acting, 4 stroke engine of 0. The length of the indicator diagram is 0. A six-cylinder, 4-stroke gasoline engine is run at a speed of RPM. The area of the indicator card of one cylinder is 2. The bore of the cylinders is mm and the piston stroke is mm. Determine the indicated power, assuming that each cylinder contributes an equal power.

A closed cylinder of 0. The volume on the other side of the piston is evacuated. A helical spring is mounted coaxially with the cylinder in this evacuated space to give a force of N on the piston in this position. The catch is released and the piston travels along the cylinder until it comes to rest after a stroke of 1. The piston is then held in its position of maximum travel by a ratchet mechanism. The spring force increases linearly with the piston displacement to a final value of 5 kN.

Calculate the work done by the compressed air on the piston. S K Mondal Chapter 3 1. The turbine speed is rpm. Determine a the torque developed by the turbine, b the power delivered to the propeller shaft, and c the net rate of working of the reduction gear.

The cylinder diameter is 0. During the stirring process lasting 10 minutes, the piston slowly moves out a distance of 0. The net work done by the fluid during the process is 2 kJ. The speed of the electric motor driving the stirrer is rpm. Determine the torque in the shaft and the power output of the motor.

If the bore and stroke of each cylinder is 0. S K Mondal Chapter 3 Solution: The macroscopic properties of the system obey the following relationship: Where a, b, and R are constants. Obtain an expression for the displacement work done by the system during a constant-temperature expansion from volume V1 to volume V2. Calculate the work done by a system which contains 10 kg of this gas expanding from 1 m3 to 10 m3 at a temperature of K.

The flow energy of 0. Find the pressure at this point. Heat leaks into the milk from the surroundings at an average rate of 4. Take the cp of milk to be 4. The specific heat of fish above freezing point is 3.

How much heat must be removed to cool the fish, and what per cent of this is latent heat? Page 28 of First Law of Thermodynamics By: S K Mondal 4. Therefore, E remains constant for such a system. The Zeroth Law deals with thermal equilibrium and provides a means for measuring temperatures. The First Law deals with the conservation of energy and introduces the concept of internal energy. The Second Law of thermodynamics provides with the guidelines on the conversion heat energy of matter into work.

It also introduces the concept of entropy. The Third Law of thermodynamics defines the absolute zero of entropy. The entropy of a pure crystalline substance at absolute zero temperature is zero. Only at infinite temperature one can dream of getting the full 1 kW work output. In other words, 0 K is unattainable.

This is precisely the Third law. Page 29 of That is why all temperature scales are at best empirical. To get work output you must give some thermal energy. To get some work output there is a minimum amount of thermal energy that needs to be given.

Violation of all 3 laws: Try to get everything for nothing. Page 30 of Nag Q4. An engine is tested by means of a water brake at rpm. The measured torque of the engine is mN and the water consumption of the brake is 0.

Calculate the water temperature at exit, assuming that the whole of the engine power is ultimately transformed into heat which is absorbed by the cooling water. What is the net work for this cyclic process? The fluid is surrounded by a perfect heat insulator during the reaction which begins at state 1 and ends at state 2. The insulation is then removed and kJ of heat flow to the surroundings as the fluid goes to state 3.

The following data are observed for the fluid at states 1, 2 and 3. Evaluate the magnitude and direction of the third heat transfer. Q3 A domestic refrigerator is loaded with food and the door closed. During a certain period the machine consumes 1 kWh of energy and the internal energy of the system drops by kJ.

Find the net heat transfer for the system. S K Mondal Q4. The same liquid as in Problem 4. During the process 1. For this fluid, find cv and cp. If there is no heat transfer, find the net work for the process. The initial Page 34 of There is no work other than that done on a piston. Find DE for the gaseous mixture. A mass of 8 kg gas expands within a flexible container so that the p—v relationship is of the from pvl.

The initial pressure is kPa and the initial volume is 1 m3. The final pressure is 5 kPa. The initial and final pressures are kPa and kPa respectively and the corresponding volumes are 0.

Calculate the net heat transfer and the maximum internal energy of the gas attained during expansion. S K Mondal Chapter 4 Solution: U max Q4. Page 37 of S K Mondal Chapter 4 b How much does the internal energy of the system increase? If the heat rejected by the engine in a cycle is kJ per kg of working fluid, what would be its thermal efficiency?

The processes are as follows: There are no significant changes in KE and PE. Page 40 of S K Mondal Chapter 5 5. Nag Q5. Find the exit air temperature, assuming adiabatic conditions. Take cp of air is 1. Pressure 1. The steam leaves the turbine at the following state: Heat is lost to the surroundings at the rate of 0. If the rate of steam flow through the turbine is 0. The nozzle is horizontal and there is negligible heat loss from it.

Velocity at exit from S. What is the cooling water flow required for cooling 2. Electric current flow is produced as a result of energy transfer as heat. In a Page 44 of S K Mondal Chapter 5 particular experiment the current was measured to be 0. Determine the rate of energy transfer as heat from the cold side and the energy conversion efficiency. During the expansion, there is a heat transfer of 0. Calculate the turbine exhaust temperature if changes in kinetic and potential energy are negligible.

The power absorbed by the compressor is 4. Determine the heat transfer in a The compressor b The cooler State your assumptions. In water cooling tower air enters at a height of 1 m above the ground level and leaves at a height of 7 m. Water enters at a height of 8 m and leaves at a height of 0. The cooling tower is well insulated and a fan of 2. The values of cp of air and water are 1. The air is compressed heated, expanded through a turbine, and exhausted at 0.

The power output is kW. There is no heat transfer to or from the gas as it flows through the compressor. One stream is supplied at the rate of 0. The other stream is supplied at the rate of 0. At the exit from the engine the fluid leaves as two Page 49 of Chapter 5 streams, one of water at the rate of 0.

The engine develops a shaft power of 25 kW. The heat transfer is negligible. Evaluate the enthalpy of the second exit stream. The stream of air and gasoline vapour, in the ratio of The engine has a specific fuel consumption of 0.

The net heat transfer rate from the fuel-air stream to the jacket cooling water and to the surroundings is 35 kW. The shaft power delivered by the engine is 26 kW. Compute the increase in the specific enthalpy of the fuel air stream, assuming the changes in kinetic energy and in elevation to be negligible. Neglecting changes in elevation, determine the magnitude and sign of the heat transfer per unit mass of air flowing.

Inlet Exit Pressure 1. A room for four persons has two fans, each consuming 0.