Question

Two cylinders A and B fitted with pistons contain equal amount of an ideal rigid diatomic gas at 303 K . The piston of cylinder \(A\) is free to move and that of cylinder B is held fixed. The same amount heat is given to the gas in each cylinder. If the rise in temperature of the gas in cylinder B is 49 K , then the rise in temperature of the gas in \(A\) is

• A. 30 K
• B. 35 K
• C. 70 K
• D. 75 K

Hint:

The same heat gives different temperature rises at constant volume and constant pressure because the molar heat capacities differ by the ratio gamma.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Cylinder B has a fixed piston, so heat goes in at constant volume: \(Q=nC_V\Delta T_B\). Cylinder A has a free piston, so \(Q=nC_P\Delta T_A\).

Step 2: Heat capacities
For a rigid diatomic gas \(C_V=\dfrac52R\) and \(C_P=\dfrac72R\).

Step 3: Equate the heat
\(nC_V\Delta T_B=nC_P\Delta T_A\) gives \(\Delta T_A=\dfrac{C_V}{C_P}\Delta T_B=\dfrac57\times49\).

Step 4: Result
\(\Delta T_A=35\text{ K}\).

Final Answer:
The temperature of gas in A rises by 35 K. \[ \boxed{\text{(B) }\text{35 K}} \]