Explanation Formula used: Write the expression for quantity of heat for constant-volume process. Q = n C V Δ T (1) Here, n is number of moles in a gas, C V is the molar specific heat at constant volume, and Δ T is the change in temperature. Write the expression for quantity of heat for constant-pressure process. Q = n C P Δ T (2) Here, n is number of moles in a gas, C P is the molar specific heat at constant pressure, and Δ T is the change in temperature. Write the expression for Δ T . Δ T = T f − T i (3) Here, T f is the final temperature, and T i is the initial temperature. Explanation: Modify equation (1) for temperature “A” as follows. Q = n C V Δ T A (4) Modify equation (2) for temperature “B” as follows. Q = n C P Δ T B (5) Modify equation (3) for temperature “A” as follows. Δ T A = ( T A ) f − ( T A ) i Modify equation (3) for temperature “B” as follows. Δ T B = ( T B ) f − ( T B ) i Substitute 10 J for Q in equation (4), 10 J = n C V Δ T A (6) Substitute 10 J for Q in equation (5), 10 J = n C P Δ T B (7) Compare equation (6) and (7). n C V Δ T A = n C P Δ T B (8) Refer to Table 12.6 in the textbook for molar specific heats of gases. In all gases the value of C V is greater than the value of C P . C V > C P If the number of moles in a gas is equal and C V > C P then equation (8) modified as follows. C V Δ T A > C P Δ T B (9) From equation (9), write the relation between T A and T B as follows

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Author: Knight

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Chapter 12, Problem 15CQ

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