Question

Two vessels $A$ and $B$ of equal volume $V_0$ are connected by a narrow tube which can be closed by a valve. The vessels are fitted with pistons which can be moved to change the volumes. Initially, the valve is open and the vessels contain an ideal gas $(C_P/C_v=\gamma )$ at atmospheric pressure $P_0$ and atmospheric temperature $T_0$. The walls of the vessels $A$ are diathermic and those of $B$ are adiabatic. The valve is now closed and the pistons are slowly pulled out to increase the volumes of the vessels to double the original value.
Find the temperatures and pressures in the two vessels.

• A. $T_0,\frac{P_0}{3}$ in vessel $A$ and $\frac{T_0}{2^{\gamma -1}},\frac{P_0}{2^{\gamma }}$.
• B. $T_0,\frac{P_0}{2}$ in vessel $A$ and $\frac{T_0}{2^{\gamma -1}},\frac{P_0}{2^{\gamma }}$.
• C. $T_0,\frac{P_0}{12}$ in vessel $A$ and $\frac{T_0}{2^{\gamma -1}},\frac{P_0}{2^{\gamma }}$.
• D. $T_0,\frac{P_0}{22}$ in vessel $A$ and $\frac{T_0}{2^{\gamma -1}},\frac{P_0}{2^{\gamma }}$.

Answer 1

The correct option is B $T_0,\frac{P_0}{2}$ in vessel $A$ and $\frac{T_0}{2^{\gamma -1}},\frac{P_0}{2^{\gamma }}$.