Question:
This question has Statement-1 and Statement-2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement 1: The internal energy of a perfect gas is entirely kinetic and depends only on absolute temperature of the gas and not on its pressure or volume.
Statement 2: A perfect gas is heated keeping pressure constant and later at constant volume. For the same amount of heat the temperature of the gas at constant pressure is lower than that at constant volume.
This question has Statement-1 and Statement-2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement 1: The internal energy of a perfect gas is entirely kinetic and depends only on absolute temperature of the gas and not on its pressure or volume.
Statement 2: A perfect gas is heated keeping pressure constant and later at constant volume. For the same amount of heat the temperature of the gas at constant pressure is lower than that at constant volume.
Statement 1: The internal energy of a perfect gas is entirely kinetic and depends only on absolute temperature of the gas and not on its pressure or volume.
Statement 2: A perfect gas is heated keeping pressure constant and later at constant volume. For the same amount of heat the temperature of the gas at constant pressure is lower than that at constant volume.
Show Hint
Check each statement separately (\(U\) of an ideal gas depends only on \(T\); \(C_p\gt C_v\)), then judge whether Statement-2 explains Statement-1.
Updated On: Oct 31, 2026
- Statement-1 is true, Statement-2 is true and Statement −2 is the correct explanation of Statement-1.
- Statement-1 is true, Statement-2 is false.
- Statement-1 is true, Statement-2 is true but Statement-2 is not the correct explanation of Statement-1.
- Statement-1 is false, Statement-2 is true.
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The Correct Option is C
Solution and Explanation
Statement-1: for an ideal (perfect) gas there are no intermolecular forces, so internal energy is purely kinetic, \(U=nC_vT\), a function of \(T\) only. True.
Statement-2: heat at constant pressure \(Q=nC_p\Delta T_p\), at constant volume \(Q=nC_v\Delta T_v\). For the same \(Q\): \(\Delta T_p/\Delta T_v=C_v/C_p=1/\gamma\lt 1\). So the temperature rise at constant pressure is smaller. True.
Statement-2 concerns the difference between \(C_p\) and \(C_v\) (part of the heat goes into work at constant pressure); it does not explain why \(U\) depends only on temperature. So it is not the correct explanation.
Answer: (3) Statement-1 is true, Statement-2 is true but Statement-2 is not the correct explanation of Statement-1.
Statement-2: heat at constant pressure \(Q=nC_p\Delta T_p\), at constant volume \(Q=nC_v\Delta T_v\). For the same \(Q\): \(\Delta T_p/\Delta T_v=C_v/C_p=1/\gamma\lt 1\). So the temperature rise at constant pressure is smaller. True.
Statement-2 concerns the difference between \(C_p\) and \(C_v\) (part of the heat goes into work at constant pressure); it does not explain why \(U\) depends only on temperature. So it is not the correct explanation.
Answer: (3) Statement-1 is true, Statement-2 is true but Statement-2 is not the correct explanation of Statement-1.
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