Question

Two cylinders $A$ and $B$ fitted with pistons contain equal amounts of an ideal diatomic gas at $300\text{K}$. The piston of $A$ 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 in temperature of the gas in $A$ is $30\text{K}$, then the rise in temperature of the gas in $B$ is:

• A. $30\text{K}$
• B. $18\text{K}$
• C. $50\text{K}$
• D. $42\text{K}$

Answer 1

The correct option is D $42\text{K}$

In cylinder $A$, gas remains at constant pressure, since the piston is free to move.
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,
$Q=n{C}_P\times 30.......\left(1\right)$

In cylinder $B$, work done by gas is zero [since volume is fixed]/
Heat given to the ideal diatomic gas in the cylinder $B$ is given by
$Q=\Delta U=n{C}_V\Delta T_2.......\left(2\right)$
From $\left(1\right)$ and$\left(2\right)$ we get,
$C_P\times 30=C_V\Delta T_2$
$\Delta T_2=\frac{C_P\times 30}{C_V}$
For a diatomic gas
$\gamma =\frac{C_P}{C_V}=\frac{7}{5}$
Thus, $\Delta T_2=\frac{7}{5}\times 30=42\text{K}$
Hence, option (d) is the correct answer.