Question

Two cylinders $A$ and $B$ having pistons contain equal amounts of an ideal diatomic gas at $300\text{K}$. The piston $A$ is free to move while the piston B is held fixed. Same quantity of heat is supplied to the gas in each cylinder. The temperature of the gas in cylinder $A$ rises by $35\text{K}$. The rise in temperature of the gas in cylinder $B$ is

• A. $51\text{K}$
• B. $49\text{K}$
• C. $47\text{K}$
• D. $45\text{K}$

Answer 1

The correct option is B $49\text{K}$

Heat given to the ideal diatomic gas in the cylinder $A$ is given by
$Q=n{C}_P\Delta T_1$
from the data given in the question,
$Q=n{C}_P\times 35............\left(1\right)$
Heat given to the ideal diatomic gas in the cylinder $B$ is given by
$Q=n{C}_V\Delta T_2..........\left(2\right)$
From $\left(1\right)$ and$\left(2\right)$ we get,
$C_P\times 35=C_V\Delta T_2$
$\Delta T_2=\frac{C_P\times 35}{C_V}$
For a diatomic gas
$\gamma =\frac{C_P}{C_V}=\frac{7}{5}$
Thus, $\Delta T_2=\frac{7}{5}\times 35=49\text{K}$
Hence, option (b) is the correct answer.