Question

Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 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

⇒ nC_PdT₁ = nC_vdT₂

From (I) and (II)

$c_{v}dT_{2} = \left( c_{v} + R \right)30$ $\therefore$ $dT_{2} = \frac{(c_{v} + R)30}{c_{v}}$

For diatomic gas $c_{v} = \frac{5}{2}R$ $\therefore dT_{2} = 42K$.