Work Done and Internal Energy PYQs: JEE Mains Physics

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1. 1. 10 mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from \(P _1\) to \(P _2\) is \(\alpha\) Joule \(\left( P _1=21.7 Pa\right.\) and \(\left.P _2=30 Pa, C _{ v }=21 J / K . mol , R=8.3 J / mol . K \right)\). The value of \(\alpha\) is _________ .
   2026 Hard
2. 2. 10 mole of oxygen is heated at constant volume from \(30^{\circ} C\) to \(40^{\circ} C\). The change in the internal energy of the gas is _________ cal. (The molecular specific heat of oxygen at constant pressure, \(C _{ p }=7 cal . / mol ^{\circ} C\) and \(\left.R =2 cal . / mol ^{\circ} C .\right)\) 2026 Medium
3. 3. A thermodynamic system is taken through the cyclic process ABC as shown in the figure (P-V graph : A(2, 100), B(5, 300), C(5, 100). The total work done by the system during the cycle ABC is ___________ J.
   2026 Medium
4. 4. Density of water at \(4^{\circ} C\) and \(20^{\circ} C\) are \(1000 kg / m ^3\) and respectively. The increase in internal energy of 4 kg water when it is heated from \(4{ }^{\circ} C\) to \(20^{\circ} C\) is _________ J.
   (Specific heat capacity of water \(=4.2 KJ / kg\). and 1 atmospheric pressure \(=10^5 Pa\) ) 2026 Hard
5. 5. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
   Statement I: Change in internal energy of a system containing \(n\) mole of ideal gas can be written as \(\Delta U = n C_v (T_f - T_i) = \dfrac{nR}{\gamma - 1}(T_f - T_i)\), where \(\gamma = \dfrac{C_p}{C_v}\), \(T_i =\) initial temperature, \(T_f =\) final temperature.
   Statement II: Relation between degree of freedom \(f\) and \(\gamma (= C_p/C_v)\) is \(\left(\gamma = 1 + \dfrac{2}{f}\right)\)
   Choose the correct answer from the options given below 2026 Medium
6. 6. In the following \(p-V\) diagram the equation of state along the curved path is given by \((V-2)^2=4\) ap where \(a\) is a constant. The total work done in the closed path is
   2026 Medium
7. 7.
   A poly-atomic molecule ( \(C_V=3 R, C_P=4 R\), where \(R\) is gas constant) goes from phase space point \(\mathrm{A}\left(\mathrm{P}_{\mathrm{A}}=10^5 \mathrm{~Pa}, \mathrm{~V}_{\mathrm{A}}=4 \times 10^{-6} \mathrm{~m}^3\right)\) to point \(\mathrm{B}\left(\mathrm{P}_{\mathrm{B}}=5 \times 10^4 \mathrm{~Pa}, \mathrm{~V}_{\mathrm{B}}=6 \times 10^{-6} \mathrm{~m}^3\right)\) to point \(\mathrm{C}\left(\mathrm{P}_{\mathrm{C}}=10^4\right.\) \(\left.\mathrm{Pa}, \mathrm{V}_{\mathrm{C}}=8 \times 10^{-6} \mathrm{~m}^3\right)\). A to B is an adiabatic path and \(B\) to \(C\) is an isothermal path. The net heat absorbed per unit mole by the system is : 2025 Hard
8. 8. An ideal gas exists in a state with pressure \(P_0\) volume \(\mathrm{V}_0\).It is isothermally expanded to 4 times of its initial volume \(\left(\mathrm{V}_0\right)\), then isobarically compressed to its original volume. Finally the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is : 2025 Medium
9. 9. An ideal gas has undergone through the cyclic process as shown in the figure. Work done by the gas in the entire cycle is ______ \(\times 10^{-1} \mathrm{~J}\).
   (Take \(\pi=3.14\))
   2025 Medium
10. 10. The magnitude of heat exchanged by a system for the given cyclic process ABCA (as shown in figure) is (in SI unit) :
    
    2025 Hard
11. 11.
    Using the given \(\mathrm{P}-\mathrm{V}\) diagram, the work done by an ideal gas along the path ABCD is : 2025 Easy
12. 12. A diatomic gas \((\gamma=1.4)\) does \(200 \mathrm{~J}\) of work when it is expanded isobarically. The heat given to the gas in the process is _______. 2024 Hard
13. 13. A gas mixture consists of \(8\) moles of argon and \(6\) moles of oxygen at temperature \(T\). Neglecting all vibrational modes, the total internal energy of the system is _______. 2024 Hard
14. 14. A thermodynamic system is taken from an original state \(A\) to an intermediate state \(B\) by a linear process as shown in the figure. It's volume is then reduced to the original value from \(B\) to \(C\) by an isobaric process. The total work done by the gas from \(A\) to \(B\) and \(B\) to \(C\) would be :
    2024 Hard
15. 15. Choose the correct statement for processes \(A\)  & \(B\) shown in figure.
    2024 Hard
16. 16. The heat absorbed by a system in going through the given cyclic process is _______.
    2024 Hard
17. 17. A thermodynamic system is taken through cyclic process. The total work done in the process is \(.........\,J\)
    2023 Easy
18. 18. The pressure of a gas changes linearly with volume from \(A\) to \(B\) as shown in figure. If no heat is supplied to or extracted from the gas then change in the internal energy of the gas will be \(............\,J\)
    2023 Medium
19. 19. A sample of an ideal gas is taken through the cyclic process \(ABCA\) as shown in figure. It absorbs, \(40\,J\) of heat during the part \(A B\), no heat during \(BC\) and rejects \(60\,J\) of heat during \(CA\). \(A\) work \(50\,J\) is done on the gas during the part \(BC\). The internal energy of the gas at \(A\) is \(1560\,J\). The work done by the gas during the part \(CA\) is.............\(J\)
    2022 Medium
20. 20. A thermodynamic system is taken from an original state \(D\) to an intermediate state \(E\) by the linear process shown in the figure. Its volume is then reduced to the original volume from \(E\) to \(F\) by an isobaric process. The total work done by the gas from \(D\) to \(E\) to \(F\) will be \(......J\)
    2022 Medium
21. 21. A diatomic gas, having \(C_{p}=\frac{7}{2} R\) and \(C _{ v }=\frac{5}{2} R ,\) is heated at constant pressure. The ratio \(dU : dQ : dW :\) 2021 Hard
22. 22. If one mole of an ideal gas at \(\left( P _{1}, V _{1}\right)\) is allowed to expand reversibly and isothermally (\(A\) to \(B\) ) its pressure is reduced to one-half of the original pressure (see \(figure\)). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value \(( B \rightarrow C ) .\) Then it is restored to its initial state by a reversible adiabatic compression (\(C\) to \(A\)). The net workdone by the gas is equal to  ...... .
    2021 Hard
23. 23. In a certain thermodynamical process, the pressure of a gas depends on its volume as \(kV ^{3}\). The work done when the temperature changes from \(100^{\circ} C\) to \(300^{\circ} C\) will be .......... \(nR\), where \(n\) denotes number of moles of a gas. 2021 Hard
24. 24. In the reported figure, heat energy absorbed by a system in going through a cyclic process is \(......\,\pi J\)
    2021 Medium
25. 25. In thermodynamics, heat and work are 2021 Medium
26. 26. \(n\) mole a perfect gas undergoes a cyclic process \(ABCA\) (see figure) consisting of the following processes. \(A \rightarrow B :\) Isothermal expansion at temperature \(T\) so that the volume is doubled from \(V _{1}\) to \(V _{2}=2 V _{1}\) and pressure changes from \(P _{1}\) to \(P _{2}\) \(B \rightarrow C :\) Isobaric compression at pressure \(P _{2}\) to initial volume \(V _{1}\) \(C \rightarrow A\) : Isochoric change leading to change of pressure from \(P _{2}\) to \(P _{1}\) Total workdone in the complete cycle \(ABCA\) is
    2021 Hard
27. 27. One mole of an ideal gas is taken through an adiabatic process where the temperature rises from \(27^{\circ} {C}\) to \(37^{\circ} {C}\). If the ideal gas is composed of polyatomic molecule that has \(4\) vibrational modes which of the following is true? 2021 Medium
28. 28. The \(P-V\) diagram of a diatomic ideal gas system going under cyclic process as shown in figure. The work done during an adiabatic process \(CD\) is (use \(\gamma=1.4\)) (in \(J\))
    2021 Medium
29. 29. A closed vessel contains \(0.1\) mole of a monoatomic ideal gas at \(200\, K\). If \(0.05\) mole of the same gas at \(400\, K\) is added to it, the final  equilibrium temperature (in \(K\) ) of the gas in the vessel will be closed to 2020 Medium
30. 30. Three different processes that can occur in an ideal monoatomic gas are shown in the \(P\) vs \(V\) diagram. The paths are labelled as \(A \rightarrow B, A \rightarrow C\) and \(A \rightarrow D .\) The change in internal energies during these process are taken as \(E _{ AB }, E _{ AC }\) and \(E _{ AD }\) and the work done as \(W _{ AB }\) \(W _{ AC }\) and \(W _{ AD }\) The correct relation between these parameters are
    2020 Hard
31. 31. A diatomic gas with rigid molecules does \(10\, J\) of work when expanded at constant pressure. What would be the heat energy absorbed by the gas, in this process ..... \(J\). 2019 Medium
32. 32. A gas can be taken from \(A\) to \(B\) via two different processes \(ACB\) and \(ADB\). When path \(ACB\) is used \(60\, J\) of heat flows into the system and \(30\, J\) of work is done by the system. If path \(ADB\) is used work down by the system is \(10\, J\). the heat flow into the system in path \(ADB\) is ..... \(J\)
    2019 Medium
33. 33. A sample of an ideal gas is taken through the cyclic process \(abca\) as shown in the figure. The change in the internal energy of the gas along the path \(ca\) is \(-180\, J\). The gas absorbs \(250\, J\) of heat along the path \(ab\) and \(60\, J\) along the path \(bc\). The work done by the gas along the path \(abc\) is ..... \(J\)
    2019 Medium
34. 34. Following figure shows two processes \(A\) and \(B\) for a gas. If \(\Delta Q_A\) and \(\Delta Q_B\) are the amount of heat absorbed by the system in two cases, and \(\Delta U_A\) and \(\Delta U_B\) are changes in internal energies, respectively, then
    2019 Medium
35. 35. For the given cyclic process \(CAB\) as shown for a gas, the work done is ..... \(J\)
    2019 Easy
36. 36. Given that \(1\,g\) of water in liquid phase has volume \(1\,cm^3\) and in vapour phase \(1671\, cm^3\) at atmospheric pressure and the latent heat of vaporization of water is \(2256\,J/g;\) the change in the internal energy in joules for \(1\,g\) of water at \(373\,K\) when it changes from liquid phase to vapour phase at the same temperature is ....... \(J\) 2019 Medium
37. 37. \(200\,g\) water is heated from \(40\,^oC\) to \(60\,^oC.\) Ignoring the slight expansion of water, the change in its internal energy is close to ...... \(kJ\) (Given specific heat of water \(=4184\,J/kgK\) ) 2016 Medium
38. 38. A gas is compressed from a volume of \(2\,m^3\) to a volume of \(1\, m^3\) at a constant pressure of \(100\, N/m^2\). Then it is heated at constant volume by supplying \(150\, J\) of energy. As a result, the internal energy of the gas 2014 Medium
39. 39. One mole of a diatomic ideal gas undergoes a cyclic process \(ABC\) as shown in figure. The process \(BC\) is adiabatic. The temperatures at \(A, B\) and \(C\) are \(400\ K, 800\ K \) and \(600\ K\) respectively. Choose the correct statement
    2014 Easy
40. 40. A sample of gas expands from \(V_1\) to \(V _2\). In which of the following, the work done will be greatest ?
    2013 Medium
41. 41. The above \(P-V\) diagram represents the thermodynamic cycle of an engine, operating with an ideal monatomic gas. The amount of heat, extracted from the source in a single cycle is
    2013 Medium

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