AIIMS 2019 Physics Specific Heats MCQ Question
Two cylinders of equal size are filled with equal amount of ideal diatomic gas at room temperature. Both the cylinders are fitted with pistons. In cylinder A the piston is free to move while in B position is fixed. When same amount of heat is supplied to both the cylinders, the temperature of the gas cylinder A raises by 30 K. What will be the rise in temperature of the gas in cylinder B.
Correct Answer
Detailed Explanation
Option B is correct because it calculates the change in temperature (ΔT) for a gas undergoing an isochoric process, using the specific heat ratio for a diatomic gas (like O₂ or N₂), which is typically 7/5. Thus, when ΔT is given as 30 °K, the calculation yields 42 °K (7/5 × 30 = 42 °K).
Option A is incorrect because it misrepresents the relationship between ΔT and the specific heats, suggesting a direct ratio that does not apply in this context. Option C is misleading as it implies that the heat transferred in both processes is equal, which is not generally true since Q_A and Q_B depend on different specific heats (Cₚ for isobaric and Cᵥ for isochoric). Option D incorrectly concludes that the heat transferred in both processes is the same, which contradicts the definitions of isobaric and isochoric processes.
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