Two cylinders A and B fitted with piston contain equal amount of an… | MHT CET 2024 (11 May, Shift 2)

Q105MHT CET 2024 · 11 MAY · SHIFT 2Medium

Thermodynamic Processes

Two cylinders A and B fitted with piston contain equal amount of an ideal diatomic as at temperature ' T ' K. The piston of cylinder A is free to move while that of B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise temperature of the gas in A is ' $dT_A$ ', then the rise in temperature of the gas in cylinder B is $\left(\gamma = \frac{C_p}{C_v}\right)$

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Answer: (c)

A (free piston) is heated at constant pressure: $Q = nC_p\,dT_A$ .
B (fixed piston) is heated at constant volume: $Q = nC_v\,dT_B$ .
Equal heat: $C_v\,dT_B = C_p\,dT_A \Rightarrow dT_B = \frac{C_p}{C_v}dT_A = \gamma\,dT_A$
So the answer is (c) $\gamma\, dT_A$ .

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