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 30 K, then the rise in temperature of the gas in B is

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

Answer 1

Answer: (D)

42 K

Answer 2

In both cylinders A and B the gases are diatomic (γ = 1.4). Piston A is free to move i.e. it is isobaric process. Piston B is fixed i.e. it is isochoric process. If same amount of heat ∆Q is given to both then

$(\Delta Q)_{\text{isobaric}} = (\Delta Q)_{\text{isochoric}}$

$\mu C_{p}(\Delta T)_{A} = \mu C_{v}(\Delta T)_{B}$

⇒ $(\Delta T)_{B} = \frac{C_{p}}{C_{v}}(\Delta T)_{A} = \gamma(\Delta T)_{A} = 1.4 \times 30 = 42K.$