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 $42\text{K}$

Heat is given to the gas in cylinder $A$ at constant pressure while the same amount of heat is given to the gas in cylinder $B$ at constant volume. Heat given to gas in $A$ is
$Q_A=n{C}_p\Delta T_A$
Heat given to gas in $B$ is $Q_B=n{C}_v\Delta T_B$
Since $Q_A=Q_B$, we have
$n{C}_p\Delta T_A=n{C}_v\Delta T_B$
or $\Delta T_B=\frac{C_p}{C_v}\Delta T_A$
$=\frac{7}{5}\times 30\text{K}=42\text{K}$
($\because$ for a diatomic gas, $C_p/C_v=7/5$)
Hence the correct choice is (d).