Question

Two cylinders A and B are fitted with pistons. A and B contain equal moles of an ideal monoatomic gas at $400K$. Piston in A is free to move, while piston in B is held fixed. Same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in A is $42K$, then the increase in the temperature of the gas in B is ($\gamma =\frac{5}{3}$):

• A. $35K$
• B. $42K$
• C. $70K$
• D. $21K$

Answer 1

Answer: (C)

$70K$

In the first case, energy supplied is equal to the change in enthalpy since pressure is constant, while in the second case, it is equal to the change in internal energy since the volume is constant.

$Q_1=n{C}_P\Delta T=n\frac{\gamma }{\gamma -1}R\Delta T_1$

$Q_2=n{C}_P\Delta T=n\frac{1}{\gamma -1}R\Delta T_2$

Hence, $\gamma \Delta T_1=\Delta T_2$

Now, $\Delta T_1=42K$, so $\Delta T_2=70K$