Question

Two cylinders fitted with piston contain equal amount 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 gas in B is

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

Answer 1

The correct option is D $42K$

In cylinder A, heat is supplied at constant pressure while in cylinder B heat is supplied at constant volume.
$(\Delta Q{)}_A=n{C}_p(\Delta T{)}_A$
and $(\Delta Q{)}_B=n{C}_v(\Delta T{)}_B$
Given : $(\Delta Q{)}_A=(\Delta Q{)}_B$
$\therefore$$(\Delta T{)}_B=\frac{C_p}{C_v}(\Delta T{)}_A$
$=1.4\times 30$
$=42K[\therefore$ for diatomic gas $\frac{C_p}{C_v}=1.4$]