Question

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

• A. $30K$
• B. $18K$
• C. $50K$
• D. $42K$

Answer 1

The correct option is D $42K$

In case $A$, since the piston is free to move,

$△Q=n{C}_p△T_1(C_p$ for diatomic gas $=\frac{7}{2}R)$

In case $B$, since volume is constant,

$△Q=n{C}_v△T_2(C_v=\frac{5}{2}R)$

Since heat given is same for both the systems

$n{C}_p△T_1=n{C}_v△T_2$

$△T_1=30$

$\frac{7}{2}\times R\times 30=\frac{5}{2}\times R\times △T_2$

$△T_2=42K$