Question

Two insulting cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at temperature 300K. The piston 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

Answer: (D)

42K

Answer 2

For cylinder A. For cylinder B

dQ = nC_PdT₁ dQ = nC_VdT₂

= n(C_V+R) dT₁

∴ nC_VdT₂ = n(C_V+R) 30

$\therefore$ $dT_{2} = \frac{(C_{v} + R)30}{C_{v}}$

For diatomic gas $C_{v} = \frac{5}{2}R$

$\therefore dT_{2} = 42K$.

Hence (4)