Question

Two cylinders A and B fitted with piston contain equal amount of an ideal diatomic gas at temperature T K. The piston of cylinder A is free to move while that of cylinder \(B\) is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise of temperature of the gas in A is \(\mathrm{dT}_{\mathrm{A}}\), then the rise in temperature of the gas in B is \(\left(\gamma=\frac{C_p}{C_v}\right)\)

• A. \(\frac{\mathrm{dT}_{\mathrm{A}}}{2}\)
• B. \(\frac{\mathrm{dT}_{\mathrm{A}}}{\gamma}\)
• C. \(\gamma dT_{A}\)
• D. \(2\mathrm{dT}_{\mathrm{A}}\)

Hint:

The free piston gives a constant-pressure process and the fixed piston a constant-volume process.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
In cylinder A the piston moves freely, so the gas is heated at constant pressure: \(Q=nC_p\,dT_A\). In cylinder B the volume is fixed: \(Q=nC_v\,dT_B\).

Step 2: Equal heat
The same heat is supplied to the same amount of gas, so \(nC_p\,dT_A=nC_v\,dT_B\).

Step 3: Calculation
\(dT_B=\dfrac{C_p}{C_v}\,dT_A=\gamma\,dT_A\).

Final Answer:
The temperature rise in B is gamma times that in A. \[ \boxed{\text{(C) }\gamma\,dT_{A}} \]