MULTIPLE CHOICE QUESTIONS

1. [2082] The efficiency of Carnot engine operating between steam point and ice point is
   a. 26.8 %
   b. 50%
   c. 73.2%
   d. 100%

2. [2081 GIE ‘A’] An ideal refrigerator is working between 0^oC and 127^oC. The coefficient of performance is
   a. 3.25
   b. 2.85
   c. 2.15
   d. 1

3. [2081 GIE ‘B’] What is the efficiency of a carnot engine working between steam point and ice point?
   a. 27%
   b. 37%
   c. 50%
   d. 75%

4. [2081 B/C] Given figure represents the block diagram of a heat engine. What is the efficiency of this engine?
   a. 25%
   b. 50%
   c. 60%
   d. 75%

5. [2081 D] An ideal heat engine working between temperatures T₁ and T₂ has efficiency [latex]\eta[/latex]. If both the temperature are raised by 50 K each, the new efficiency of engine will be
   a. [latex]\eta[/latex]
   b. more than [latex]\eta[/latex]
   c. Less than [latex]\eta[/latex]
   d. depends upon the nature of working substance

6. [2080 GIE A] When the door of a refrigerator is left open in a room, the temperature of the room
   a. Increases
   b. Decreases
   c. Remains same
   d. First increases, then decreases

7. [2080 GIE B] An ideal refrigerator is working between 0^oC and 127^oC. The coefficient of performance is
   a. 1
   b. 2.15
   c. 2.85
   d. 3.15

8. [2080 P] A Carnot engine is working between 300 K and 600 K has output 200 J. What is the energy supplied to the engine?
   a. 400 J
   b. 800 J
   c. 1200 J
   d. 1600 J
9. [2080 R] What is the significance of the Clausius statement of the second law of thermodynamics?
   a. Defines the maximum theoretical efficiency of a heat engine.
   b. States that heat cannot be spontaneously flow from a colder object to a hotter object.
   c.   Describes the relationship between entropy and the reversibility of a process.
   d.   Describes the direction of spontaneous change in an isolated system.
10. [2079 GIE A] The efficiency of a carnot engine working between steam point and ice point is about.
    a.   56.8%              b. 44.8%                      c. 26.8%                      d. 14.8%
11. [2079 GIE B] The efficiency of a carnot engine working between 27^oC and 127^oC is
    a.   50%                 b. 100%                       c. 25%                         d. 75%
12. [2079 ‘O’] The maximum efficiency of an engine operating between 30^oC and 300^oC is,
    a.   4.71%              b. 47%             c. 90%             d. 9%              
13. [2079 ‘V’] A carnot cycle includes
    a.   Two isothermal and two adiabatic processes.
    b.   Two isothermal and two isobaric processes.
    c.   Two isothermal processes.
    d.   Two adiabatic processes.                      

Answers:

1.a	2.c	3.a	4.b	5.c	6.a	7.b	8.a	9.b	10.c
11.c	12.b	13.a

THEORETICAL QUESTIONS

1. [2080 GIE A] Draw a PV diagram of a petrol engine and explain its working based on the PV diagram.               [3]
2. [2080 P] Can a room be cooled by leaving the door of an electric refrigerator open? Justify.  [1]
3. [2080 R] Obtain the efficiency of a heat engine.                               [2]

Old Course
SHORT ANSWER QUESTION

4. [2074 ‘S’] Why does a refrigerator consume more power in summer than in winter to cool the same quantity of food by same degree?
5. [2074 ‘A’] Why not an ideal heat engine is cent percent efficient?
6. [2073 ‘S’] An engine cannot have 100% efficiency. Why and which basic expression of thermodynamic law suggest this?
7. [2073 ‘C’] Explain the significance of second law of thermodynamics.
8. [2072 ‘A’] Entropy is defined in the second law of thermodynamics. Can the first law be expressed in terms entropy? How?

LONG ANSWER QUESTION

9. [2076 ‘B’] Describe the working principle of diesel engine with the help of PV diagram.
10. [2075 ‘GIE’] State and explain second law of thermodynamics. Define the efficiency of a heat engine and explain quantitatively why the efficiency of such an engine is always less than 100%?
11. [2075 ‘B’] Describe the working principle of petrol engine with the help of its PV diagram.
12. [2073 ‘D’] What is efficiency of a heat engine? Describe the working of a petrol engine with the help of its P-V diagram.
13. [2072 ‘S’] Describe the working of a petrol engine with the help of its P-V diagram.
14. [2072 ‘C’] Describe the working of diesel engine with a P-V diagram. What are its merits and demerits?

NUMERICAL PROBLEMS

New Course

1. [2082] A Carnot’s engine has 25% efficiency with a sink at 9^oC. By how many degrees should the temperature of the source be increased in order to raise the efficiency to 50%? [3] Ans: 188 K
2. [2081 GIE ‘A’] For a carnot ideal engine, temperature of sink at temperature 27^oC and source is at temperature 127^oC. Calculate its efficiency. [3] Ans: 25%
3. [2081 D] A refrigerator has a coefficient of performance of 1.95. In each cycle, it absorbs [latex]3\times 10^4[/latex] J of heat from cold reservoir. How much heat is discarded to the high temperature during each cycle?                                 [2] Ans: [latex]4.5\times 10^4\ J[/latex]
4. [2080 GIE B] Two carnot engines A & B have their sources at 400 K and 350 K, and sinks at 350 K and 300 K respectively. Which engine is more efficient and by how much?             [2] Ans: B is more efficient than A by 1.78%
5. [2079 GIE B] A carnot engine takes [latex]4.2\times 10^6\ J[/latex] of heat from reservoir at 627^oC and performs external work. The remaining energy is rejected into a sink at 27^oC. What is the efficiency? How much work does it perform?                [1 + 1] Ans: [latex]2.8\times 10^6\ J[/latex]
6. [2079 ‘V’] A Carnot engine working between 300 K and 600 K has a working output of 800 J per cycle. What is the amount of heat energy supplied to the engine by the source per cycle?  [3] Ans: 1600 J/cycle

Old Course

7. [2076 GIE A] A carnot engine takes 10³ calories of heat from a reservoir at 227^oC and rejects heat to a reservoir at 27^oC. How much work is done by it?           Ans: 1680 J
8. [2076 GIE B] A diesel engine performs 2500 J of mechanical work and discards 4000 J of heat each cycle.
         i.    How much heat must be supplied to the engine each cycle?
         ii.   What is the thermal efficiency of the engine?     Ans: 6500 J, 38.46%
9. [2076 ‘C’] The efficiency of a Carnot cycle is 15%. If on reducing the temperature of sink by 65^oC, the efficiency becomes double, find the temperature of source and sink. Ans: 433.3 K, 368.3 K
10. [2075 ‘A’] A carnot engine has 40% efficiency with sink at 10^oC. By how many degrees should the temperature of the source be increased in order to raise the efficiency to 65%?  Ans: 336.9 K
11. [2074 ‘S’] A Carnot engine has 50% efficiency with a sink at 9^oC. By how many degrees should the temperature of source be increased in order to raise the efficiency to 70%?  Ans: 376K
12. [2074 ‘A’] An ideal heat engine operates between two reservoirs at two temperatures. In order to achieve 30% efficiency when the temperature of the sink is 50^oC, what should be the temperature of the source? Ans: 461.43 K
13. [2074 ‘B’] The source reservoir of a carnot engine is at a temperature of 400 K and takes 400 J of heat and rejects 20 J of heat to the sink reservoir in each cycle. What is the efficiency of engine and the temperature of the sink? Ans: [latex]\eta = 95\%,\ T_2\ =\ 20K[/latex]
14. [2073 ‘C’] A Carnot engine has 25% efficiency with a sink at 9^oC. By how many degrees should the temperature of the source be increased in order to raise the efficiency to 70%?  Ans: 564 K
15. [2072 ‘D’] A diesel engine performs 2200 J of mechanical work and discards 4300 J of heat each cycle. (i) How much heat must be supplied to the engine in each cycle? (ii) What is the thermal efficiency of the engine? Ans: 6500 J, 33.85%
16. [2072 ‘E’] What will be the thermal efficiency of an engine if it takes 8 KJ heat from the source and rejects 6 KJ to the sink in one cycle? Ans: 25%