Question

Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at $300K$. Piston of A is free to move and piston of B is fixed. Same amount of heat is given to the gases in two cylinders. Temperature of the gas in cylinder A increases by $30K$. Then, increase in temperature of the gas in the cylinder B is:
($\gamma =1.4$ for diatomic gas)

• A. $36K$
• B. $54K$
• C. $42K$
• D. $24K$

Answer 1

Answer: (C)

$42K$

Since the piston of A is free to move, the pressure inside the cylinder A remains the same. Thus, for given heat $H$ to the system,

$H=n{C}_P\Delta T_1$

The piston in cylinder B is fixed. Thus volume remains constant.

$H=n{C}_V\Delta T_2$

$⟹\frac{\Delta T_2}{\Delta T_1}=\frac{C_P}{C_V}$

$=1.4$

$⟹\Delta T_2=42K$