8231_23984_td q.bank 14-15 (1) (1)

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K L UNIVERSITY DEPARTMENT OF MECHANICAL ENGINEERING 13 ES 201 – THERMODYNAMICS QUESTION BANK – Course Coordinator – Dr.K.Rama Krishna 2 (1) A piston-cylinder device operates 1 kg of air at 20 bar pressure. The initial volume is 0.04 m 3 . The fluid is allowed to expand reversibly following a process pV 1.45 = constant so that the volume becomes double. The fluid is then cooled at constant pressure until the piston comes back to the original position. Keeping the piston unaltered, heat is added reversibly to restore it to the initial pressure. Calculate the work done by the cycle and its efficiency. (6+4) Apply C3 2 (2) A piston and cylinder machine containing a fluid system has a stirring device in the cylinder. The piston is frictionless, and it is held down against the fluid due to the atmospheric pressure of 101.325 kPa. The stirring device is turned 10,000 revolutions with an average torque against the fluid of 1.275 mN. Meanwhile the piston of 0.6 m diameter moves out 0.8m. Find the net work transfer for the system. Page 66 pk nag (10) Apply C3 2 (3) (a) Prove that internal energy is a point function. (4) (b) A mass of gas is compressed in a quasi- static process from 80 kPa, 0.1 m 3 to 0.4 MPa, 0.03 m 3 . Assuming that the pressure and volume are related by pv n = constant, find the work done by the gas system. Page 75 (6) Apply Apply C4 C3 2 (4) (a) Derive the expression to determine heat transfer in a reversible polytropic process. (4) (b) If air of volume 6000 cm 3 and at pressure of 100 kPa is compressed quasistatically according to pV 2 = constant until the volume becomes Apply C3

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Page 1: 8231_23984_TD Q.Bank 14-15 (1) (1)

K L UNIVERSITYDEPARTMENT OF MECHANICAL ENGINEERING

13 ES 201 – THERMODYNAMICS QUESTION BANK – Course Coordinator – Dr.K.Rama Krishna

2 (1) A piston-cylinder device operates 1 kg of air at 20 bar pressure. The initial volume is 0.04 m3. The fluid is allowed to expand reversibly following a process pV1.45 = constant so that the volume becomes double. The fluid is then cooled at constant pressure until the piston comes back to the original position. Keeping the piston unaltered, heat is added reversibly to restore it to the initial pressure. Calculate the work done by the cycle and its efficiency. (6+4)

Apply C3

2 (2) A piston and cylinder machine containing a fluid system has a stirring device in the cylinder. The piston is frictionless, and it is held down against the fluid due to the atmospheric pressure of 101.325 kPa. The stirring device is turned 10,000 revolutions with an average torque against the fluid of 1.275 mN. Meanwhile the piston of 0.6 m diameter moves out 0.8m. Find the net work transfer for the system. Page 66 pk nag (10)

Apply C3

2 (3) (a) Prove that internal energy is a point function. (4) (b) A mass of gas is compressed in a quasi-static process from 80 kPa, 0.1 m3 to 0.4 MPa, 0.03 m3. Assuming that the pressure and volume are related by pvn = constant, find the work done by the gas system.

Page 75 (6)

Apply

Apply

C4

C3

2 (4) (a) Derive the expression to determine heat transfer in a reversible polytropic process. (4) (b) If air of volume 6000 cm3 and at pressure of 100 kPa is compressed quasistatically according to pV2 = constant until the volume becomes 2000 cm3, determine the final pressure and the work transfer. (6)

Apply C3

2 (5) (a) Derive the expression for non-flow work of a closed system. State its limitations. (4) (b) An electric generator coupled to a windmill produces an average electrical power output of 5kW. The power is used to charge a storage battery. Heat transfer from the battery to the surroundings occurs at a constant rate of 0.6 kW. Determine the total amount of energy stored in the battery, in kJ, in 8h of operation. Page 93 pk nag (6)

Apply C3

2 (6) (a) A mass of 1.5 kg of air is compressed in a quasi-static process from 0.1 MPa to 0.7 MPa for which pv = constant. The initial density of air is 1.16 kg/m3. Find the work done by the piston to compress the air. (5)

(b) A thermometer is calibrated in such a way that it reads 320N when placed in melting ice and 2120N when placed in boiling water. What will it read when the measured temperature is 2880K (5)

5M

Apply

C3

C2

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2 (7) (a) If a gas of volume 6000 cm3 and at pressure of 100 kPa is compressed quasi-statically according to pV2 = constant until the volume becomes 2000 cm3, determine the final pressure and the work transfer. (5)

(b) A gas contained in a piston cylinder arrangement expands from 0.75m3 volume to 1.25m3 volume while the pressure remains constant at 200kPa. If the gaseous system receives 80kJ of work from a paddle wheel, determine the net work done by the system. (5)

Apply C3

2 (8) (a) Distinguish between Macroscopic and Microscopic points of view of thermodynamic system investigation. (4)

4M (b) What are different forms of work energy? Explain each briefly.

ApplyUnderstand

C1

C3

2 (9) (a) 1 kg of gas at 2400C expands adiabatically so that its volume is doubled and the temperature falls to 1150C . The work done during the expansion is 89.86 kJ. Calculate the two specific heats.

(5)5M

(b) State Zeroth law of thermodynamics. Briefly explain how it forms the basis for temperature measurement. (5)

5M

Apply

Understand

C3

C2

2 (10) A spherical balloon contains air at a pressure of 1.5 bar. The diameter of the balloon is increased to 40 cm by heating and during the process the pressure is proportional to its diameter. Calculate the work done assuming the process to be quasi static. (10)

Apply C3

3 (1) (a) State first law of thermodynamics applied to a closed system undergoing cyclic process. (3) (b) A stationary closed system containing air goes through a cycle comprising the following processes:

(i) Process 1-2 isochoric heat addition of 235 kJ/kg; (ii) Process 2-3 adiabatic expansion to its original pressure

with loss of 70 kJ/kg in internal energy; (iii) Process 3-1 isobaric compression to its original volume

with heat rejection of 200 kJ/kg Show that this cycle obeys first law and find its thermal efficiency. (4+3)

Apply C4

3 (2) (a) State first law applied to a change of state undergone by a closed system. (3) (b) A stationary system consisting of 2 kg of the fluid expands in an adiabatic process according to pv1.2 = constant. The initial conditions are 1 MPa and 200oC and the final pressure is 0.1 MPa. Find W and ∆E for the process. Why is the work transfer not equal to (5+2)

Apply

Analyze

C4

3 (3) (a) Define Enthalpy. (4) (b) A fluid contained in a cylinder receives 150 kJ of mechanical energy by means of a paddle wheel, together with 50 kJ in the form of heat. At the same time, a piston in the cylinder moves in such a way that the pressure remains constant at 200 kN/m2 during the fluid expansion from 2m3 to 5m3. What is the change in internal energy, and in enthalpy? Q)4.19 (6)

Understand

Apply

C4

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3 (4) (a) Define Internal Energy. (4) (b) A gas undergoes a thermodynamic cycle consisting of three processes beginning at an initial state where p1 = 1 bar, V1 = 1.5 m3 and U1 = 512 kJ. The processes are as follows:

(i)Process 1-2 : Compression with pV = constant to p2 = 2 bar, U2 = 690 kJ

(ii) Process 2-3 : W23 = 0, Q23 = -150 kJ, and (iii) Process 3-1: W31 = + 50kJ. Neglecting KE and PE changes, determine the heat interactions Q12 and Q31. Q)4.17 (6)

Apply C4

3 (5) A gas of mass 1.5 kg undergoes a quasi-static expansion which follows a relationship p = a + bV, where a and b are constants. The initial and final pressures are 1000 kPa and 200 kPa respectively and the corresponding volumes are 0.20 m3 and 1.20 m3. The specific internal energy of the gas is given by the relation

U = 1.5 pv – 85 kJ/kg Where p is the kPa and v is in m3/kg. Calculate the net heat transfer and the maximum internal energy of the gas attained during expansion. (4+6)

Apply C4

3(6) A gas undergoes a thermodynamic cycle consisting of the following processes:

(i) Process 1–2: Constant pressure p = 1.4 bar, V1 = 0.028 m3, W12 = 10.5kJ

(ii) Process 2–3: Compression with pV = constant, U3 = U2

(iii) Process 3–1: Constant volume, U1 – U3 = – 26.4 kJ. There are no significant changes in KE and PE.

(a) Sketch the cycle on a p–V diagram(b) Calculate the net work for the cycle in kJ.(c) Calculate the heat transfer for process 1–2.(d) Show that cycle ∑ Q = ∑ W (10)

Cycle cycle 10M

Apply C4

3 (7) (a) A mass of 8 kg gas expands within a flexible container so that the p–v relationship is of the from pvl.2 = constant. The initial pressure is 1000 kPa and the initial volume is 1 m3. The final pressure is 5 kPa. If specific internal energy of the gas decreases by 40 kJ/kg, find the heat transfer in magnitude and direction. (6) 6M

(b) Can we use the equation dQ=dU+dw for any irreversible process undergone by a closed system (4)

Apply

Justify

C4

C6

3Page

95Pk

nag

(8) (a) A stationary system consisting of 2 kg of the fluid of Problem 4.8 expands in an adiabatic process according to pv1.2 = constant. The initial conditions are 1 MPa and 200°C, and the final pressure is 0.1 MPa. Find W and ΔE for the process. Why is the work transfer not equal to ∫pdV? (7)

7M (b) Derive an expression for heat transfer in non-flow constant Volume process. (3)

3M

Analyze

Apply

C3

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3Page

95 Pk

nag

(9) A slow chemical reaction takes place in a fluid at the constant pressure of 0.1 MPa. 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 105 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.

State v (m3 ) t (°C)1 0.003 202 0.3 3703 0.06 20

For the fluid system, calculate E2 and E3, if E1 = 0. (10)10M

Apply C4

3 (10) (a) Prove that energy is a property of the system. (4) (b) 5 kg of air at 40° C and 1 bar is heated in a reversible non-flow constant pressure process until the volume is doubled. Find (i) work done (ii) change in internal energy and (iii) change in entropy. (6)

Apply

C3

C7

4 (1) Air flows steadily at the rate of 0.4 kg/s through an air compressor, entering at 6m/s with a pressure of 1 bar and a specific volume of 0.85 m3/kg, and leaving at 4.5 m/s with a pressure of 6.9 bar and a specific volume of 0.16 m3/kg. The internal energy of the air leaving is 88 kJ/kg greater than that of the air entering. Cooling water in a jacket surrounding the cylinder absorbs heat from the air at the rate of 59 W. Calculate the power required to drive the compressor and the inlet and outlet cross-sectional areas. (5+3+2)

Application C5

4 (2) Air flows steadily through a rotary compressor. The gas enters the compressor at a temperature of 16oC, a pressure of 100 kPa, and an enthalpy of 391.2 kJ/kg. The gas leaves the compressor at a temperature of 245oC, a pressure of 0.6 MPa, and an enthalpy of 534.5 kJ/kg. There is no heat transfer to or from the gas as it flows through the compressor. (a) Evaluate the external work done per unit mass of gas assuming the gas velocities at entry and exit to be negligible. (b) Evaluate the external work done per unit mass of gas when the gas velocity at entry is 80 m/s and that at exit is 160 m/s. (10)

Evaluate C5

4 (3) (a) Derive the steady flow energy equation. (4) (b) A turbo compressor delivers air @ 2.33m3/s at 0.276 MPa, 43oC which is heated at this pressure to 430oC and finally expanded in a turbine which delivers 1860 kW. During the expansion, there is a heat transfer of 0.09 mJ/s to the surroundings. Calculate the turbine exhaust temperature if changes in kinetic and potential energy are negligible. (6)

Apply C5

4 (4) In a gas turbine the gas enters at the rate of 5 kg/s with a velocity of 50 m/s and enthalpy of 900 kJ/kg and leaves the turbine with a velocity of 150 m/s and enthalpy of 400 kJ/kg. The loss of heat from the gases to the surroundings is 25 kJ/kg. Assume for gas R = 0.285 kJ/kg K and cp = 1.004 kJ/kgK and the inlet conditions to be at 100 kPa and 27oC. Determine the power output of the turbine and the diameter of the inlet pipe. (10)

Apply C5

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4 (5) (a) What is the significance of the term PV in the expression H=U+PV. Explain. (4) (b) A turbine operates under steady flow conditions, receiving steam at the following state: pressure 1.2 MPa, temperature 188oC, enthalpy 2785 kJ/kg, velocity 33.3 m/s and elevation 3m. The steam leaves the turbine at the following state: pressure 20 kPa, enthalpy 2512 kJ/kg, velocity 100 m/s, and elevation 0 m. Heat is lost to the surroundings at the rate of 0.29 kJ/s. If the rate of steam flow through the turbine is 0.42 kg/s, what is the power output of the turbine in kW? (6)

Understand

Apply C5

4 (6) Steam enters a horizontal nozzle at an enthalpy of 2764.85 kJ/kg, a specific volume of 0.25547 m3/kg, a temperature of 2800C and at a steady velocity of 40 m/s. At the exit, the steam has the enthalpy and specific volume of 2755.5 kJ/kg and 0.31546 m3/kg, respectively. If the nozzle is adiabatic and if the diameter of the nozzle at the inlet is 15 cm, calculate (i) the velocity of steam at the exit, (ii) the rate of flow of steam per second and (iii) the exit diameter of the nozzle. (10)

10M

Apply C5

4 (7) (a) A blower handles 1 kg/s of air at 20°C and consumes a power of 15 kW. The inlet and outlet velocities of air are 100m/s and 150m/s respectively. Find the exit air temperature, assuming adiabatic conditions. Take cp of air is 1.005 kJ/kg K. (5)

5M (b) Make an energy analysis for a steam nozzle and heat exchanger. (5)

Apply

Analyze

C5

4 (8) Derive an Expression for SFEE. Discuss its application to compressors and nozzles. (6+4)

6+4MApply C5

4 (9) (a) A turbine operates under steady flow conditions, receiving steam at the following state: Pressure 1.2MPa, temperature 188°C, enthalpy 2785kJ/kg, velocity 33.3m/s and elevation 3m. The steam leaves the turbine at the following state: Pressure 20kPa, enthalpy 2512kJ/kg, velocity 100m/s, and elevation 0m. Heat is lost to the surroundings at the rate of 0.29kJ/s. If the rate of steam flow through the turbine is 0.42 kg/s, what is the power output of the turbine in kW? (6)

6M (b) State the importance of boundary in thermodynamics? (4)

Apply

Understand

C5

C1

4 (10) Air at 10/.325 kPa, 20oC is taken into a gas turbine power plant at a velocity of 140 m/s through an opening of 0.15 m2 cross-sectional area. The air is compressed heated, expanded through a turbine, and exhausted at 0.18 MPa, 150oC through an opening of 0.10 m2 cross- sectional area. The power output is 375 kW. Calculate the net amount of heat added to the air in kJ/kg. (10)

C5

5 (1) A heat pump is used to maintain an auditorium hall at 24° C when the atmospheric temperature is 10° C. The heat lost from the hall is 1500 kJ/min. Calculate the power required to run the heat pump if its COP is 30% of Carnot machine working between the same temperature limits.

(10)

Apply C6

5 (2) A heat pump working on the Carnot cycle takes in heat from a reservoir at 5oC and delivers heat to a reservoir at 60oC. The heat pump is driven by a reversible heat engine which takes in heat from a reservoir at 840oC and rejects heat to a reservoir at 60oC. The reversible heat engine also drives a machine that absorbs 30kW. If the heat pump extracts 17 kJ/s from the 5oC reservoir, determine (a) the rate of heat supply from the 840oC source, and (b) the rate of heat rejection to the 60oC sink.

Apply C6

Page 6: 8231_23984_TD Q.Bank 14-15 (1) (1)

(5+5)

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5 (3) 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. The efficiency of the heat engine is 27% and the COP of the heat pump is 4. Evaluate the ratio of the heat transfer to the circulating water to the heat transfer to the heat engine. (10)

Evaluate C6

5 (4) (a) What is a PMM2. (4) (b) 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 fQ2 at T2. The heat pump abstracts Q4 from the sink at T4 and discharges Q3 at T3. Develop an expression for the ratio Q4/Q1 in terms of the four temperatures. (6)

Remember

ApplyC6

5 (5) A reversible cyclic heat engine operates between the maximum and minimum temperatures of 671oC and 60oC respectively. It drives a heat pump which uses river water at 4.4oC to heat a block of flats in which the temperature is to be maintained at 21.1oC. Assuming that a temperature difference of 11.1oC exists between the working fluid and the river water, on the one hand, and the required room temperature on the other, and find the heat input to the engine per unit heat output from the heat pump. Why is direct heating thermodynamically more wasteful? (10)

Apply C6

5 (6) (a) State the assumptions made by Carnot in developing Carnot Engine. (4) (b) 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. Show that for a given power output and a given T1, the area of the radiator will be a minimum

when (6)

Understand

Apply C5

5 (7) (a) Two reversible heat engines 1 and 2 are connected in series such that 1 is rejecting heat directly to 2. Engine 1 receives 200 kJ at a temperature of 421oC from a hot source, while Engine 2 is in communication with a cold sink at a temperature of 4.4oC. The work output of 1 is two times that of 2. Calculate (i) the intermediate temperature between 1 and 2, (ii) the efficiency of each engine, and (iii) the heat rejected to the cold sink. (6) (b) State and prove Clausius inequality (4)

Apply C6

5 (8) (a) 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. The efficiency of the heat engine is 27% and the COP of the heat pump is 4. Evaluate the ratio of the heat transfer to the circulating water to the heat transfer to the heat engine. (5)

5M (b) State and prove Carnot’s theorem (5)

Apply C6

5 (9) A heat pump working on the Carnot cycle takes in heat from a reservoir at 5°C and delivers heat to a reservoir at 60°C. The heat

pump is driven by a reversible heat engine which takes in heat from a reservoir at 840°C and rejects heat to a reservoir at 60°C. The reversible heat engine also drives a machine that absorbs 30 kW. If the heat pump extracts 17 kJ/s from the 5°C reservoir, determine

(i) The rate of heat supply from the 840°C source

Apply C6

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(ii)The rate of heat rejection to the 60°C sink. (10)5 (10) A household refrigerator is maintained at a temperature of 2°C.

Every time the door is opened, warm material is placed inside, introducing an average of 420 kJ, but making only a small change in the temperature of the refrigerator. The door is opened 20 times a day, and the refrigerator operates at 15% of the ideal COP. The cost of work is Rs. 2.50 per kWh. What is the monthly bill for this refrigerator? The atmosphere is at 30°C. (10)

Apply C6

6 (1) (a) Explain (i) Availability (ii) Second law efficiency. (4) (b) One kg of air is contained in a rigid tank at 500 kPa and 700° K. The dead state is taken as 20° C and 100 kPa. Calculate maximum useful work (i) if the system were to change to dead state. (ii) when air is cooled to 400° K in the tank. (6)

Understand

ApplyC8

6 (2) (a) What do you understand by the terms availability and unavailability? (4) (b) Eighty kg of water at 100oC are mixed with 50 kg of water at 60oC, while the temperature of the surroundings is 150C. Determine the decrease in available energy due to mixing. (6)

Understand

Apply C8

6 (3) (a) Define Entropy and state its physical significance. (3) (b) Air flows through an adiabatic compressor at 2 kg/s. The inlet conditions are 1 bar and 310 K and the exit conditions are 7 bar and 560 K. Compute the net rate of availability transfer and the irreversibility. Take T0 =298 K. (5+2)

Understand

Apply

C7

C8

6 (4) (a)Show that Mixing is always irreversible using principle of Entropy. (4)

(b)A reversible engine, as shown in Fig. during a cycle of operations draws 5 MJ from the 400 K reservoir and does 840 kJ of work. Find the amount and direction of heat interaction with other reservoirs. (6)

Q3 Q2 Q1 = 5 MJ

W=840 kJ

Apply C7

6 (5) Calculate the entropy change of the universe as a result of the following processes:

(a) A copper block of 600gm and with Cp of 150 J/K at 100o C is placed in a lake at 8oC.

(b) The same block, at 8oC, is dropped from a height of 100m into the lake.

(c) Two such blocks, at 100 and 0oC, are joined together. (10)

Apply C7

6 (6) (a) What do understand by Clausius inequality? Explain. (4) (b) Two kg of water at 80oC are mixed adiabatically with 3 kg of water at 30oC in a constant pressure process of 1 atmosphere. Find the increase in the entropy of the total mass of water due to the mixing process (cp of water = 4.187 kJ/kg K). (6)

Understand

Apply C7

200 K 300 K 400 K

E

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6 (7) (a) The volume of 1 kg of air increases from 0.5 m3 to 1.3 m3 while its pressure decreases from 1 MPa to 0.25 MPa. Then 100 KJ of heat is added to it is a constant pressure process. Calculate the entropy change for the whole events. Assume for air CP = 1.005 KJ/KgK and R = 0.287 KJ/KgK. (6) (b) 1250 KJ of heat is supplied to a reversible cyclic engine at 527oC. The surrounding are at 20oC. Find the available energy and unavailable energy. (4)

Apply

C7

C8

6 (8) (a) 5 kg of air at 1.3 bar and 27oC is compressed to 24 bar pressure according to the law PV1.33

= C. After compression air is cooled at constant volume at 30oC. Determine i) Change of entropy during compression and ii) change of entropy during constant volume cooling. For air take CP=1.01 and CV = 0.72. (5) (b) 2 kgs of water at 50oC is mixed with 3 kgs of water at 100oC in a steady flow process calculate (a) the mixture temperature (b) in mixing reversible or irreversible (c) what is the unavailable energy w.r.t the reservoir at 50oC. (5)

Apply

C7

C8

6 (9) (a) A Carnot engine operates between 1000 K and 300 K. The change in entropy of the source is 0.6 KJ/K. Find the heat added and net work output. (4) (b) An ideal gas R = 0.2 KJ/kgk is throttled adiabatically from 12.2 bar 37oC to 1 bar. If the surroundings are at 27oC find the irreversibility of the process in KJ/Kg. (6)

Apply

C7

C8

6 (10) (a) Explain the principle of increase of entropy. (3) (b) Calculate the entropy change of the universe as a result of the

following processes: (i) A copper block of 600 g mass and with Cp of 150 J/K

at 100°C is placed in a lake at 8°C. (ii) The same block, at 8°C, is dropped from a height of 100 m into

the lake. (iii) Two such blocks, at 100 and 0°C, are joined together. (3+2+2)

Understand

Apply C7

7 (1)(a) Derive the equation

= and hence (6)

(b) Prove that cv of an ideal gas is a function of T only. (4)

Apply C9

7 (2) Derive the third TdS equation

TdS = Cv dp + Cp dV

and hence prove that

TdS = Cv dT + (10)

Apply C9

7 (3) Derive the equation using Maxwell’s relations.

-T (10)Apply C9

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7 (4) Show that equation

Cp – Cv = -T (10) Apply C9

7 (5) Derive the equations

(a) Cp = T (5)

(b) (5)

Apply C9

7 (6) Using Maxwell’s relations deduce the two TdS equations. (10) Analyze C97 (7) If entropy S be imagined as a function of T and V, then show that

dS = cv (dT/T) + (∂p/∂T)v dV (10) Apply C9

7 (8) If entropy S be imagined as a function of T and p, then show that TdS = cp dT - T( ∂V/∂T )p dp (10)

Apply C9

7 (9) Prove that cp – cv = - T (∂V/∂T)p2 x (∂p/∂V)T (10) Apply C9

7 (10) (a) Derive the equation

= and hence (6)

(b) Prove that cv of an ideal gas is a function of T only. (4)

Apply C9

8 (1) (a) Compare Otto and Diesel cycle for the same compression ratio and same heat rejection. (4) (b) In an air standard Otto cycle the compression ratio is 7, and compression begins at 35oC, 0.1 MPa. The maximum temperature of the cycle is 1100oC. Find (a) the work done per kg of air, (b) the cycle efficiency. (6)

Evaluate

ApplyC10

8 (2)In an air standard Diesel cycle, the compression ratio is 15. Compression begins at 0.1 MPa, 40oC. The heat added is 1.675 MJ/kg. Find (a) the maximum temperature of the cycle, (b) the work done per kg of air, (c) the cycle efficiency, (d) the cut-off ratio, (e) the m.e.p. of the cycle. (10)

Apply C10

8 (3) In an air standard Brayton cycle the compression ratio is 7 and the maximum temperature of the cycle is 800oC. The compression begins at

0.1 MPa, 35oC. Compare the maximum specific volume and the maximum pressure with the Otto cycle. Find (a) the heat supplied per kg of air, (b) the net work done per kg of air, (c) the cycle efficiency, and (d) the temperature at the end of the expansion process. (10)

Analyze C10

8 (4) A gas turbine plant operates on the Brayton cycle between the temperatures 27oC and 800oC. (a) Find the pressure ratio at which the cycle efficiency approaches the Carnot cycle efficiency, (b) find the pressure ratio at which the work done per kg of air is maximum, and (c) compare the efficiency at this pressure ratio with the Carnot efficiency for the given temperatures. (10)

Analyze C10

8 (5) (a) Derive the expression for efficiency of an Otto cycle in terms of compression ratio. (4) (b) In an air standard Diesel cycle, the compression ratio is16, and at the beginning of isentropic compression, the temperature is 15oC and the pressure is 0.1 MPa. Heat is added until the temperature at the end of the constant pressure process is 1480oC. Calculate (a) the cut-off ratio, (b) the cycle efficiency, and (c) the m.e.p. (6)

Apply C10

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8 (6) A dual combustion cycle operates with a volumetric compression ratio rk = 12, and with a cut-off ratio 1.615. The maximum pressure is given by pmax = 54p1, where p1 is the pressure before compression. Assuming indices of compression and expansion of 1.35, show that the m.e.p. of the cycle pm = 10 p1. Hence evaluate (a) temperatures at cardinal points with T1 = 335 K, and (b) Cycle efficiency. (10)

Evaluate C10

8 (7) Show that the air standard efficiency for a cycle comprising two constant pressure processes and two isothermal processes (all reversible) is given by

η =

Where T1 and T2 are the maximum and minimum temperatures of the cycle, and rp is the pressure ratio. (10)

Apply C10

8 (8) Two engines are to operate on Otto and Diesel cycles with the following data: Maximum temperature 1400 K, exhaust temperature

700 K. State of air at the beginning of compression 0.1 MPa, 300 K. Estimate the compression ratios, the maximum 0.2 pressures, efficiencies, and rate of work outputs (for 1 kg/min 0.3 of air) of the

respective cycles. (10)

Analyze C10

8 (9) Helium is used as the working fluid in an ideal Brayton cycle. Gas enters the compressor at 27°C and 20 bar and is discharged at 60 bar. The gas is heated to l000°C before entering the turbine. The cooler returns the hot turbine exhaust to the temperature of the compressor inlet. Determine: (a) the temperatures at the end of compression and expansion, (b) the heat supplied, the heat rejected and the net work per kg of He, and (c) the cycle efficiency and the heat rate. Take Cp = 5.1926 kJ/kg K. (10)

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8 (10) (a) Derive an expression for air standard efficiency of a Diesel cycle. (4) (b) An engine operating on ideal Otto cycle for which the following information is available:

Maximum temperature : 1277° CExhaust temperature : 447° CAmbient conditions : 1 bar and 37° CAir consumption : 2 kg/min

Estimate (i) Air standard efficiency and (ii) power output. Take Cp = 1.005 kJ/kg and Cv = 0.718 kJ/kg. (6)

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