Heat Engine and Carnot Cycle PYQs: JEE Mains Physics

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1. 1. A Carnot engine \((\mathrm{E})\) is working between two temperatures 473 K and 273 K . In a new system two engines - engine \(E_1\) works between 473 K to 373 K and engine \(E_2\) works between 373 K to 273 K .If \(\eta_{12}, \eta_1\) and \(\eta_2\) are the efficiencies of the engines \(E, E_1\) and \(E_2\), respectively, then 2025 Medium
2. 2. A Carnot engine operating between two reservoirs has efficiency \(\frac{1}{3}\). When the temperature of cold reservoir raised by \(x\), its efficiency decreases to \(\frac{1}{6}\). The value of \(x\), if the temperature of hot reservoir is \(99^{\circ}\,C\), will be \(........\,K\) 2023 Medium
3. 3. A Carnot engine with efficiency \(50\,\%\) takes heat from a source at \(600\,K\). In order to increase the efficiency to \(70\,\%\), keeping the temperature of sink same, the new temperature of the source will be \(.........\,K\) 2023 Medium
4. 4. An engine operating between the boiling and freezing points of water will have \(1.\) efficiency more than \(27 \%\) \(2.\) efficiency less than the efficiency a Carnot engine operating between the same two temperatures. \(3.\) efficiency equal to \(27 \%\) \(4.\) efficiency less than \(27 \%\) 2023 Medium
5. 5. Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason \(R\). Assertion A : Efficiency of a reversible heat engine will be highest at \(-273^{\circ} C\) temperature of cold reservoir. Reason \(R\) : The efficiency of Carnot's engine depends not only on temperature of cold reservoir but it depends on the temperature of hot reservoir too and is given as \(\eta=\left(1-\frac{ T _2}{ T _1}\right)\). In the light of the above statements, choose the correct answer from the options given below 2023 Medium
6. 6. Work done by a Carnot engine operating between temperatures \(127^{\circ}\,C\) and \(27^{\circ}\,C\) is \(2\,kJ\). The amount of heat transferred to the engine by the reservoir is \(........\,kJ\) 2023 Medium
7. 7. \(300 \,cal\). of heat is given to a heat engine and it rejects \(225 \,cal\). of heat. If source temperature is \(227^{\circ} C\), then the temperature of sink will be____\({ }^{\circ} C\). 2022 Medium
8. 8. A Carnot engine has efficiency of \(50 \%\). If the temperature of sink is reduced by \(40^{\circ} C\), its efficiency increases by \(30 \%\). The temperature of the source will be\(....K\) 2022 Medium
9. 9. A Carnot engine take \(5000 \,k\,cal\) of heat from a reservoir at \(727\,^{\circ}C\) and gives heat to a \(\operatorname{sink}\) at \(127\,^{\circ}C\). The work done by the engine is \(.......... \times 10^{6}\,J\) 2022 Medium
10. 10. A Carnot engine whose heat \(\operatorname{sinks}\) at \(27\,^{\circ} C\), has an efficiency of \(25 \%\). By how many degrees should the temperature of the source be changed to increase the efficiency by \(100 \%\) of the original efficiency \(?\) 2022 Hard
11. 11. A heat engine operates with the cold reservoir at temperature \(324 K\). The minimum temperature of the hot reservoir, if the heat engine takes \(300 \; J\) heat from the hot reservoir and delivers \(180 \; J\) heat to the cold reservoir per cycle, is \(\dots \; K .\) 2022 Medium
12. 12. Consider the efficiency of Carnot's engine is given by \(\eta=\frac{\alpha \beta}{\sin \theta} \log _{e} \frac{\beta x}{k T}\), where \(\alpha\) and \(\beta\) are constants. If \(T\) is temperature, \(k\) is Boltzman constant, \(\theta\) is angular displacement and \(x\) has the dimensions of length. Then, choose the incorrect option. 2022 Hard
13. 13. In \(1^{\text {st }}\) case, Carnot engine operates between temperatures \(300\,K\) and \(100\,K\). In \(2^{\text {nd }}\) case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in \(2^{\text {ad }}\) case) will be.
    2022 Medium
14. 14. In a carnot engine, the temperature of reservoir is \(527^{\circ} C\) and that of \(\operatorname{sink}\) is \(200 \; K\). If the workdone by the engine when it transfers heat from reservoir to sink is \(12000 \; kJ\), the quantity of heat absorbed by the engine from reservoir is \(\times 10^{6} \; J\) 2022 Medium
15. 15. Let \(\eta_{1}\) is the efficiency of an engine at \(T _{1}=447^{\circ}\,C\) and \(T _{2}=147^{\circ}\,C\) while \(\eta_{2}\) is the efficiency at \(T _{1}=947^{\circ}\,C\) and \(T _{2}=47^{\circ}\,C\). The ratio \(\frac{\eta_{1}}{\eta_{2}}\) will be. 2022 Medium
16. 16. The efficiency of an ideal heat engine working between the freezing point and boiling point of water, is ........ \(\%\) 2022 Medium
17. 17. A Carnot's engine working between \(400\, K\) and \(800\, K\) has a work output of \(1200\, J\) per cycle. The amount of heat energy supplied to the engine from the source in each cycle is ........... \(J\) 2021 Medium
18. 18. A heat engine operates between a cold reservoir at temperature \({T}_{2}=400\, {K}\) and a hot reservoir at temperature \({T}_{1} .\) It takes \(300 \,{J}\) of heat from the hot reservoir and delivers \(240\, {J}\) of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be \(....{K}\) 2021 Medium
19. 19. A reversible engine has an efficiency of \(\frac{1}{4}\). If the temperature of the sink is reduced by \(58^{\circ} {C}\), its efficiency becomes double. Calculate the temperature of the sink. (In \(^{\circ} {C}\)) 2021 Hard
20. 20. A reversible heat engine converts one-fourth of the heat input into work. When the temperature of the sink is reduced by \(52\, K\), its efficiency is doubled. The temperature in Kelvin of the source will be ...... . 2021 Medium
21. 21. For an ideal heat engine, the temperature of the source is \(127\,^{\circ} C\). In order to have \(60\, \%\) efficiency the temperature of the sink should be \(........\,{ }^{\circ} C\). (Round off to the Nearest Integer) 2021 Medium
22. 22. Two carnot engines \(A\) and \(B\) operate in series such that engine \(A\) absorbs heat at \(T_{1}\) and rejects heat to a sink at temperature \(T\). Engine \(B\) absorbs half of the heat rejected by engine \(A\) and rejects heat to the sink at \({T}_{3}\). When workdone in both the cases is equal, the value of \({T}\) is  2021 Hard
23. 23. A Carnot engine operates between two reservoirs of temperatures \(900\; \mathrm{K}\) and \(300 \;\mathrm{K}\) The engine performs \(1200\; \mathrm{J}\) of work per cycle. The heat energy (in \(\mathrm{J}\) ) delivered by the engine to the low temperature reservoir, in a cycle. is 2020 Medium
24. 24. A heat engine is involved with exchange of heat of \(1915\, J,\) \(-40\, J ,+125\, J\) and \(-Q\,J\), during one cycle achieving an efficiency of \(50.0 \%\). The value of \(Q\) is.......\(J\) 2020 Medium
25. 25. An engine operates by taking a monatomic ideal gas through the cycle shown in the figure. The percentage efficiency of the engine is close to  \(.......\%\)
    2020 Hard
26. 26. Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperatures, \(\mathrm{T}_{1}\) and \(\mathrm{T}_{2} .\) The temperature of the hot reservoir of the first engine is \(\mathrm{T}_{1}\) and the temperature of the cold reservoir of the second engine is \(\mathrm{T}_{2} . T\) is temperature of the sink of first engine which is also the source for the second engine. How is \(T\) related to \(\mathrm{T}_{1}\) and \(\mathrm{T}_{2}\), if both the engines perform equal amount of work? 2020 Medium
27. 27. Three Carnot engines operate in series between a heat source at a temperature \(T_1\) and a heat sink at temperature \(T_4\) (see figure). There are two other reservoirs at temperature \(T_2\) and \(T_3\), as shown, with \(T_1 > T_2 > T_3 > T_4\). The three engines are equally efficient if
    2019 Hard
28. 28. Two Carnot engines \(A\) and \(B\) are operated in series. The first one, \(A,\) receives heat at \(T_1(= 600\,K)\) and rejects to a reservoir at temperature \(T_2.\) The second engine \(B\) receives heat rejected by the first engine and, in turns, rejects to a heat reservoir at \(T_3 (=400\,K).\) Calculate the temperature \(T_2\) if the work outputs of the two engines are equal   ..... \(K\) 2019 Medium
29. 29. Two Carnot engines \(A\) and \(B\) are operated in series. Engine \(A\) receives heat from a reservoir at \(600\,K\) and rejects heat to a reservoir at temperature \(T\). Engine \(B\) receives; heat rejected by engine \(A\) and in turn rejects it to a reservoir at \(100\,K\). If the efficiencies of the two engines \(A\) and \(B\) are represented by \({\eta _A}\) and \({\eta _B}\) respectively, then what is the value of \(\frac{{{\eta _A}}}{{{\eta _B}}}\) 2018 Hard
30. 30. An engine operates by taking \(n\,moles\) of an ideal gas through the cycle \(ABCDA\) shown in figure. The thermal efficiency of the engine is : (Take \(C_v =1 .5\, R\), where \(R\) is gas constant)
    2017 Hard
31. 31. The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is 2016 Medium
32. 32. A Carnot engine absorbs \(1000\,J\) of heat energy from a reservoir at \(127\,^oC\) and rejects \(600\,J\) of heat energy during each cycle. The efficiency of engine and temperature of sink will be 2014 Hard

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