Question-47 Two cylinders A and B fitted with pistons contain equal amount of an ideal rigid atomic gas at 303 K. The piston of cylinder A is free to move and that of cylinder 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 cylinder B is 49 K, then the rise in temperature of the gas in A is
(A) 30 K
(B) 35 K
(C) 70 K
(D) 75 K
Answer : (B)
Explanation:
In cylinder A, heat is supplied at constant pressure while in B at constant volume
Q_A = Q_B
n C_p dT_A = n C_v dT_B
dT_B = \frac{C_p}{C_v} dT_A
⇒ dT_B = γ dT_A
⇒ 49 = \frac{7}{5} dT_A ….(∵ γ for rigid diatomic gas is \frac{7}{5})
⇒ dT_A = 35 K