MHB Multiple choices question on specific heats of gases

[WMDhamnekar]

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

My answer is 42 K. Is this answer correct?

 

[HOI]

Okay, what do YOU understand about this problem? You titled it "specific heat" so you must know that specific heat has something to do with this. How is specific heat of a gas related to its temperature?

 

[WMDhamnekar]

Okay, what do YOU understand about this problem? You titled it "specific heat" so you must know that specific heat has something to do with this. How is specific heat of a gas related to its temperature?

The piston in the cylinder A is free to move. Hence pressure of the gas is constant and the heat is given to it at constant pressure. that means $ Q_A=nC_p \Delta T_A$ where,
Q is the heat supplied or needed to bring about a change in temperature ($\Delta T$) in 1 mole of a substance ;
n is the amount of gas in moles;
$C_p$ is the molar heat capacity of a body of given substance at constant pressure.

The piston of the cylinder B is fixed. Hence the volume of the gas is constant and the heat is given at constant volume i.e., $ Q_B= nC_v \Delta T_B$ where $C_v$ is the molar heat capacity of a body of substance at constant volume.
The ratio of specific heats for a diatomic gas is $\frac{C_p}{C_v}=\frac75=1.4$. The heat given to the two gases are equal, $Q_A =Q_B$
So,
$\Delta T_B = \frac{C_p}{C_v}\Delta T_A= 42 K$

 

[I like Serena]

Looks good to me.