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: Formula first
$\Delta T_A=\dfrac{\Delta T_B}{\gamma}$ with $\gamma=\dfrac{7}{5}$ for a rigid diatomic gas.

Step 2: Substitution
$\Delta T_A=\dfrac{49}{1.4}=35\text{ K}$.

Step 3: Check
Constant pressure needs more heat per degree because the gas also does work, so its rise is smaller than 49 K. This fits 35 K.

Final Answer:
The rise in temperature in A is 35 K. \[ \boxed{\text{(B) }\text{35 K}} \]