Answer to Question #147296 in Molecular Physics | Thermodynamics for Sridhar

Question

Two cylinders A and B of equal capacity are connected to each other via a stopcock. Cylinder A contains an ideal gas at standard pressure P . The cylinder A&B are in thermal contact with a reservoir at temperature T. The stopcock is suddenly opened. After the gas reaches equilibrium the pressure P' is related to the original pressure P by
Ans:P'=P

Answer 1

Let's consider a situation when the equilibrium is reached. We have gas in cylinder A with volume $V_1=V$. The volume of the gas in cylinder B is $V_2 = V$ (because A and B are of equal capacity). Both cylinder are connected to reservoir at temperature T. According to the 0th law of thermodynamics, the temperature will equal in all tree reservoirs $T_1 = T_2 = T_3 = T'$.

So, we have that gases in A and B have equal volumes and temperatures.

According to the Mendeleev Clapeyron equation, $pV = n RT$ , if V and T are equal, P must be equal as well.

So, $P = P'$