Unit 01 QUESTION BANK
1. Define Engineering thermodynamics. Give applications of it.
2. State Zeroth law of thermodynamics
3. What is thermometer list most commonly used thermometer
4. What is an international fixed point? How it is being fixed?
5. Explain Measurement of temperature or temperature scale.
Tutorial problems:
- In 1703 sir Isack Newton proposed a linear temperature scale for which he choose the ice point and human point temperature as the two fixed point and assigned numerical values of 0oS and 100oS respectively. If the human body temperature is in centigrade 36oC. Obtain the relation between Newton scale and oC.( Ans:Tos = 2.77 toC , ToC = 0.36 toN.)
- Fahrenheit, Celsius thermometer both immersed in fluid. Fahrenheit reading numerically twice that of centigrade reading. What is temperature of fluid expressed as oR and oK.(Ans:ForoF = 2oC ,T= 446.7 R,)
3. The e.m.f in a thermocouple is 0V when the test junction is at 0oC (ice point) and 12 V when it is at steam point. Find the temperature of the system when e.m.f is 3V. Use the relation.( Ans: t = 6.25oC.)
University Questions
Problems:
- The readings TA and TB of two Celsius thermometers A and B agree at ice point and steam point. But else where are related by equation tA = L + MtB + N.Where, L.M.N are constant. When both thermometers are immersed in a system of fluid. A registers 11oC while B registers 10oC. Determine the reading on A when B registers 37.4oC.
ii. Which thermometer is correct.( VTU-Nov 2007)
- The Temperature t on a certain Celsius thermometric scale is given by means of a property through a relation t = a ln p + b Where a and b are constants and p is the property of the fluid .If at the ice point and steam points the values of pare found to be 4 and 20 respectively, What will be temperature reading corresponding to a reading of p = 16(VTU Dec 08 / Jan 09 )
- The resistance of the windings in a certain motor is found to be 80 Ohms at room temperature ( 250º ) .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 980 ohms. The windings are made of copper whose resistance at temperature tº C is given by Rt = R0 [ 1+ 0.00393 t ] When R0 is the resistance at 0 º C .Find the temperature attained by the coil during full load.( VTU-June /July 08)
Theory:
4. Mention the Characteristics of a thermodynamic Property (Dec 08/ Jan 09)
5. Differentiate between the following with suitable examples (June/July 2008)
i. System and control volume
ii. Intensive and Extensive Properties
iii. Path and Point function
6. Define the following (June/July 2008)
i. Thermodynamic state
ii. Quasi-Static Process
iii. Cyclic and Non – Cyclic Process.
7. Distinguish between (Dec /Jan 2008)
i. Open system and closed system
ii. Macroscopic and Microscopic approach
iii. Point function and path function
iv. Intensive and extensive properties
v. Diathermic and adiabatic walls
unit 2 question bank
Theory Questions:
- Define Work and Heat.
- Write the similarities and dissimilarities between work and heat.
- How do you say heat and work are path functions?
- Derive the work done for polytrophic and adiabatic process.
- Draw and explain the pdv equation formation to solve the Quasi static process, and explain about the Sign convention for compression and expansion process
Tutorial Problems:
- An engine cylinder has a piston area 0.12 m2 and contains gas at a pressure 1.5 MPa. The gas expands according to a process which is represented by a straight line on a pressure volume diagram. The final pressure is 0.15 MPa. Calculate work done by the gas on the piston if the piston stroke is 0.3 m.
( Ans:29.7 KJ
2.A system of volume V contains a mass m kg of gas at pressure P and temperature
T. The pressure volume and temperature of gas are related by equation.
(V – b) = mRT
Where, a,b,R are constants obtain an expression for the displacement work when
system is undergoing an isothermal process from V1 to V2, calculate the
displacement work. If m = 10 kg, T = 293 k and the gas expands from 1 m3 to 10
m3 at atmospheric pressure. Assume that
A = 15.7 104 Nm4,B = 1.07 10-2 m3, R = 0.278 KJ/Kg K.
( Ans := 1.74 MJ.)
3. An Engine cylinder of dia. (22.5 Cm) has a stroke length 37.5 Cm. Swept volume is 4 times the clearance volume. The pressure of gases at the beginning of expansion stroke is 1569 KPa. Find the work done during an expansion stroke assuming the process as reversible adiabatic take = 1.4.(Ans:W1-2 == 6.97 MJ.)
University Problems:
1. A gaseous system undergoes a process of quasi-static process in sequence from state 1 to 2 at constant pressure between state 2 to 3. The system undergoes compression process.(PVn = C)Between state 3 to 1 the gas expands according to (PV = C). TakeP1 = 1 bar,V1 = 0.3 m3 ,P3 = 4 bar,V2 = 0.2 m3
Calculate the work interaction in each of this process and net work for the system.
(Result: Wnet = 7.37 KN – m )-VTU July 2008
2.1 Kg of air having an initial volume of 0.3 cubic meters is heated at constant pressure of 3.2 bar until the volume is doubled. Calculate
1. Heat added. 2. Work done 3.initial and final temperature of the air.
Take,CP = 1.003 KJ/ Kg K ,R = 0.2927 KJ / Kg K.
(Result: W net == 96 KJ.)VTU Dec 2007
3.1 Kg of air contained in a closed system at 100 KPa and 300 K is compressed isothermally till the volume halves. During this process it is also stirred with a torque of 1 Nm at 400 rPm for 1 hr. Calculate the net work done on the system. Assume R = 0.285 KJ/ KgK. (Result: (Wnet)System = W1 + W2, = - 59.26 + 150.796, = - 210 KJ.)VTU Jan 2008
4. As an engineering student suggest the most economical process when it is desired to compress one mole of air (γ =1.4) from an initial state of 300 K and 1 bar to a final state of 300 K and 10 bar from an initial state of 300 K and 1 bar to final state of 300 K and 10 bar from among the following processes:
a. Isothermal compression
b. Cooling at constant pressure followed by heating at constant volume
c. Adiabatic compression followed by cooling at constant volume and
d. Heating at constant volume followed by cooling at constant pressure Take the value of R= 8.314 j / mol K.( VTU Dec / Jan 2008 )
5. A fluid at 0.7 bar occupying 0.09 m3 is compressed reversibly to a pressure of 3.5 bar according to a law PVn = Constant .The fluid is then heated reversibly at constant volume until the pressure is 4 bar ,The specific volume is then 0.5 m3 /Kg .A reversible expansion according to a law PV2 constant ,restore the fluid to its initial state .Sketch the cycle on P-V- diagram and calculate
(i) The mass of the fluid (ii) The value of ‘n’ in the first process (iii) The net work of the cycle.( VTU June /July 08)
6.A Cylinder contains 1 Kg of a certain fluid at an initial pressure of 20 bar .The fluid is allowed to expand reversibly behind a piston according to PV2 = constant unti l the volume is doubled .The fluid is then cooled reversibly at constant pressure until the piston regains its original position ; heat is then supplied reversibly with the piston firmly locked in piston until the pressure rises to the original value 20 bar .Calculate the net work done by the fluid ,for an initial volume of 0.05 m3 ( VTU Dec / Jan 08 )
Unit 3 Question bank
Theory Questions:
1. State first law of thermodynamics applied to a cyclic process
2. Define internal energy and prove that it is a property
3. What are the limitations of first law of thermodynamics?
4. Explain Law of conservation of mass
5. Define mass and volume flow rate .How do they differ.
6. What is flow energy? Do fluids at rest posses any flow energy?
7. When is the flow through a control volume steady?
8. Write down the steady flow energy equation and indicate clearly the meaning of each term in it (VTU feb 2002)
9. Derive an expression for work done in a steady flow process
10. Write down steady flow energy equation for
a) Air compressor b) Steam nozzle
Numerical problems:
1. A fluid system undergoes processes a-b, b-c, c-d, and d-a to complete a cycle, during one cycle, the total negative heat transfer is 84 kj. The system completes 100 cycles per minute .The energy transfers are tabulated below.
Process§Q (KJ / min)§W (KJ/min)dU (KJ/min)
A – b0-20945 ?
B – c209450?
C – d2094?37700
D – a ?? ?
Complete the table showing your method of calculation for each item and find the net heat by KW.
Ans:
Process§Q (KJ / min)§W (KJ/min)dU (KJ/min)
A – b0-20945 20945
B – c209450 20945
C – d2094 -3560637700
D – a-31439 48151 -79590
2. A closed system undergoes a process during which a heat transfer of 30 kj takes place from the system while 5 kj of work is done by the system .If the system is returned to the initial state by understanding another process during which there is heat transfer of 20 kj to the system .Calculate the work done in the second process.
( Ans: U2-U1 = 35 kj, work = -15 Kj )
3. A steam turbine receives steam with a flow rate of 900 kg per minute and experience a heat loss of 840 kj per minute .The exit pipe is 3 meter below the level of the inlet pipe. Find the power developed by the turbine if the pressure decrease from 62 bar to 9.86 Kpa velocity increases from 30.5 m/s to 274.3 m/s internal energy decreases by 938.8 kj/kg and specify volume increases from 0.058 m3 / kg to 13.36 m3 / kg.(Vtu –Feb 2002 )
(Ans : m = 15 kg/sec , Q = -14 kj/ sec , U2 – U1 = -938.5 kj/kg, W = 16924.66 KW )
3. A nozzle is a device for increasing the velocity of a steadily flowing stream. At the inlet to a certain nozzle, the enthalpy of the fluid passing is 3000 kj/kg and velocity is 60 m/s .At the discharge end, the enthalpy is 2762 kj/kg .The nozzle is horizontal and there is negligible heat loss from it.
Find
(i)Find the velocity at the exit section of the nozzle
(ii)If the inlet area is 0.1 m2 and the specific volume at inlet is 0.178 m3 / kg find the mass flow rate.
(iii)If the specific volume at the exit of the nozzle is 0.498 m3 /kg find the diameter at the exit section of the nozzle.
(VTU July 2004)
Ans (i) V2 = 692.53 m/s , (ii)v 1 = 0.187 m3 / kg , m =32.08 kg/s,(iii) d2 = 17.1 cm )
4.Air enters an adiabatic horizontal nozzle at 400 º C with a velocity of 50 m/s .The inlet area is 240 m2 .The temperature of air at the exit is 80ºC .Given that the specific volume of air at inlet and exit are respectively 0.2 m3/kg and 1.02 m3/kg .Find the area of cross section of the nozzle at the exit .Assume that enthalpy of air is a function of temperature only and that Cp = 1.005 kj/kg k.
(VTU July 2006)
Ans: A2 = 76.16 cm2
5.A fluid flows through a steady flow system at the rate of 3 kg/sec the inlet and outlet conditions are P1 = 5 bar ,V1 = 150 m/sec ,U1 = 2000 kj/kg and P2 = 1.2 bar , V2 =80 m/sec and U2 = 1300 kj/kg .The change in specific volume is from 0.4 m3 /kg to 1.1 m3/kg .Fluid loose 25 kj/kg heat during the process ,Neglecting potential energy determine power output of the system.
(VTU Jan 2007) Ans: W = 751 KW
Unit 04 Question bank:
Theory:
1. Write the Kelvin –planks and Clausius statement of second law of thermodynamics and prove that they are equivalent (VTU march 2000, Aug 2000,aug 2002 ,Feb 2003 ,Aug 2003 )
2. Define irreversibility and mention at least 3 factors which render a process irreversible.
3. Give precisely the Kelvin –Plank statement of second law that two reversible adiabatic paths cannot intersect each other. (VTU feb 2004)
4. State Carnot theorem (VTU aug 2000)
5. Show by invoking Kelvin –Plank statement of second law that two reversible adiabatic paths cannot intersect each other.
6. Explain the various reasons of irreversibility.(VTU Aug 2001)
7. Define the two statements of II law of thermodynamics. Show that violation of clausius statement of II law of thermodynamics violates the Kelvin –plank statement of II law of thermodynamics. (VTU, Jan 2007)
8. Define heat engine draw a neat schematic flow diagram of the steam power plant .Name the important parts and states of the working fluid .Indicates the system boundary, heat and work interaction to justify your definition (VTU, Feb 2002)
9. Define a reversible heat engine, show that of all reversed heat engines working between any two constant but different temperature thermal reservoirs, the reversible reversed heat engine will have the maximum COP. (VTU feb 2005)
10. Demonstrate, using the second law, that free expansion is an irreversible process.
11. Prove that COP Heat Pump = 1+COP refrigerator. (VTU, Jan 2007)
Numerical problems:
1. A reversible heat engine works between the two reservoirs at 1400 K and 350 K respectively. A reversible heat pump receives heat from the reservoir at 250 K and rejects the heat to a reservoir at 350 K to which the heat engine also rejects the heat .The work output from the engine is used to drive the heat pump .if the total heat supplied to the reservoir at 350 K is to be 100 KW, Find the heat to be received by the heat engine.
(Ans: Q1 = 34.78KW Heat to be received by the engine)(VTU, Jan, 2007).
2. Two reversible engine A and B are connected in series, Engine A receives heat energy from a thermal reservoir at T1 and rejects at a temperature T2 while engine B receives heat energy at T2 (at which rejected by engine A) and rejects to a thermal reservoir at T5.If both engines are equal efficient, show that the intermediate temperature T2 if both engines are delivering equal power? (Ans: T2 = (T1+T3) / T2 ) (VTU, Jan, 2007).
3. A reversible engine works between three thermal reservoirs A, B, C. The engine absorbs an equal amount of heat from the thermal reservoirs A and B Kept at temperature TA and TB respectively, and rejects heat to a thermal reservoir C kept at temperature Tc .The efficiency of this engine is α times the efficiency of a reversible engine which works between the two reservoirs A and C .Show that
TA / TB = (2α – 1) +2(1-α) (TA / TC) (VTU, Aug 2004)
4. An inventor claims that his engine has the following specifications
Power developed = 76 KW
Fuel burnt per hour = 4 kg
Heating value of fuel = 75000kj/kg
Temperature limits = 727 ºC and 27ºC
Discuss the possibility of the claim.( Ans: η thermal = 91.2 ٪ , η reversible = 70 ٪)
(VTU Aug .2000)
5. An inventor claims to have developed a refrigerator which maintains the refrigerated space at -10 ºC While operating in room at 25 ºC and it has a COP of 8.5 .How would you evaluate his claim as patent officer.(Ans : 8.76 The claim is valid )
(VTU March 2000)
6. A reversible heat engine operates with two environments .In the first it draws 12000 KW from a source at 400 ºC and in the second it draws 25000 KW from a source at 100 ºC .In both the operations the engine rejects heat to a thermal sink at 20ºC.Determine the operation in which the engine delivers more power.( Ans: thermal efficiency =56.5 percentage, Work done = 6780 Kj/s,For the second engine thermal efficiency = 21.4 percentage, Work done =5350 Kj/sec ) (VTU ,Feb ,2004 )
ADDITIONAL PROBLEMS:
1. 2Kg of nitrogen is heated at constant volume until the pressure is doubled. Calculate the heat transferred and change in entropy. Draw the PV and T-S Diagram. Initial temperature is 300 0C. R=300 J/KgK and Cv =800 J/KgK.
2. A system executes a cyclic process during which there are four heat transfers as
Given below. Q12 =800KJ Q23 = -100Kj Q34 = -720kJ Q41 =200kJ
Workdone during the three processes are given as W12 = 60kJ W23 = - 40kJ
W34 = 80kJ Find the workdone during the process 41.
3. A heat engine is supplied with 278 kJ/sec of heat at a constant fixed temperature of
2830C and the heat rejection takes place at 50C. The following results were
Reported:
(1)208 kJ/sec of heat are rejected
(2)139 kJ/sec of heat are rejected
(3)70 kJ/sec of heat rejected
Classify which of these results report a reversible cycle or impossible result.
4.5 kg of Nitrogen are heated in a reversible non-flow constant volume process from
a temperature of
600C until the pressure is doubled. Determine (i) Final temperature
(ii)Work done (iii) Change in internal energy (iv) Heat transferred
(v) Change in enthalpy (vi) Change in entropy. Assume Cv=0.653 KJ/kgK
and CP=0.913 KJ/kgK.
5. Certain volume of gas at 57 0C is expanded to three times its original volume
according to PV1.25 =C. Determine the temperature at the end and change in
entropy per kg of gas. Cp=0.99 KJ/kgK; Cv=0.7 KJ/kgK
6. An engine is to operate between temperature limits of 14000C and 3270C. It
is claimed that its power output is 4.0Kw, fuel consumption is 0.45kg/hour.
Calorific value of fuel is 42,000Kj/kg. State whether the claim is justified by
comparing with Carnot cycle.
7. Air undergoes a cyclic process in a cylinder and piston arrangement. First
the atmospheric air at 1bar 270C is compressed adiabatically to 10bar, then
expanded isothermally upto initial pressure, then brought to initial
conditions under constant pressure, find out
(ii)Change in internal energy
(iii)Change in enthalpy
(iv)Heat transfer
(v)Work transfer for each process and also for the cycle
Unit 05 Questioin Bank
Theory:
1. Derive Clausius inequality and hence prove that entropy is a property. ( VTU , March 2000 , Aug,2002 )
2. Derive an expression for entropy (VTU Aug, 2001)
3. Explain available of a system with heat transfer (VTU, March 2000)
4. State and prove Clausius theorem.(VTU ,Aug 2003 )
5. Define an inequality of clausius and entropy of a system .Show that for an irreversible process ds greater than or equal to dq / T .( VTU Jan 2007)
6. Briefly explain what do you understand by reversibility in thermodynamics, and mention at least 2 factors that render a process irreversivble.(VTU,Aug 2005 )
7. Show that the change in entropy during an irreversible process between the two states is given by (S2-S1 ) ≥ ∫ dq/T
Numerical problems:
1. A heat engine receives 125 Kj of heat/cycle from a reservoir at 300ºC and rejects heat to a reservoir at 0ºC by the following hypothetical amounts
(1) 95 Kj/cycle (2) 59.5KJ.ycle (3) 31kj/cycle.Which of these represents reversible, irreversible and impossible cycles? (VTU, March 2000)
2. Two Kg of air at 5 bar and 80ºC expands adiabatically in a closed system until its volume is doubled and the temperature becomes equal to that of the surroundings which is at 1 bar and 5ºC, Determine the maximum work (VTU, Feb 2002)
3. An insulated cylinder of capacity 4 cm2 contains 20 kg of air ( Cv = 0.718 Kj / Kg ºK
Cp = 1.005 Kj/Kg ºK) Peddle work is done on the air by stirring till its pressure increase from 4 bar to 8 bar ,Determine (1) Change in internal energy (2)Work done (3)Heat transferred (4)Change in entropy (VTU,Feb 2003 )
4.Two Kg of water at 80ºC is mixed adiabatically with three kg of water at 30ºC in a constant pressure process at one atmosphere .Find the increase in entropy of the total mass of water due to mixing process.(Assume Cp = 4.187 Kj/Kg K)(VTU ,Aug 2003 )
5. Five kg of air 555ºK and 4 bars is enclosed in a system.
(1) Determine the availability of the system if the surrounding temperature and pressure 290ºC and 1 bar respectively
(2) If the air is cooled at constant pressure to the atmosphere and pressure and if Cp = 1.005 Kj/Kg ºK ,Cv = 0.718 Kj/Kg ºK for air .Determine the available and effectiveness
(VTU, Feb, 2003)
Unit 6 Question bank
Theory:
1. Define first law and second law efficiency
2. Analyze second law efficiency fir
(i)Heat engne(ii)Heat pump(iii)Refrgerator(iv)Heat exchanger
3. Write short notes on Helmholtz anf gibbs function (VTU,Aug2000,Feb 2003)
4. Explain briefly available and unavailable energy (VTU, Aug.2001, and Feb 2003)
5. State and prove the clausius theorem (VTU, Aug.2001, and Aug2003)
6. Derive an expression for Entropy (VTU, Aug.2001)
7. What do you understand by availability of system? Explain the terms Gibbs free energy and Helmoholtz free energy.(VTU,Aug,2002)