Two containers of equal volume are connected by a stopcock as shown below.One container is filled with a gas at a pressure of 1 atm and temperature of 293 K while the other container is evacuated so that it is under vacuum.The containers are thermally isolated from the surrounding so no heat enters or escaped from the system.The stopcock is then opened allowing the gas from one container to fill the other.What is the final temperature of the gas after it has come to equilibrium?
A)136.5 K
B)273 K
C)293 K
D)195 K
E)undetermined

Question

Two containers of equal volume are connected by a stopcock as shown below.One container is filled with a gas at a pressure of 1 atm and temperature of 293 K while the other container is evacuated so that it is under vacuum.The containers are thermally isolated from the surrounding so no heat enters or escaped from the system.The stopcock is then opened allowing the gas from one container to fill the other.What is the final temperature of the gas after it has come to equilibrium? 
A)136.5 K 
B)273 K 
C)293 K 
D)195 K 
E)undetermined

Quizplus · Accepted Answer

Since the containers are thermally isolated, there is no heat transfer between them. Therefore, the total amount of gas and the total volume of the containers remain constant. When the stopcock is opened, the gas from the container with 1 atm pressure expands into the vacuum container until the pressure in both containers is the same. Since the volumes of the containers are equal, the pressure in both containers will be 0.5 atm at equilibrium.

According to the ideal gas law, PV=nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the absolute temperature. Since the amount of gas is constant, we can write

P1V1=P2V2

where P1 is the initial pressure, V1 is the initial volume, P2 is the final pressure, and V2 is the final volume.

Substituting the values, we get

1 atm x V = 0.5 atm x V

or V cancels out, and we get P1/2 = 0.5

Therefore, the pressure has decreased by a factor of 2. Using the ideal gas law again, we get

P1V1/nR = P2V2/nR

or T1 = T2

since n and R are constants, and the volumes are the same.

Therefore, the final temperature is the same as the initial temperature, which is 293 K. Thus, the correct answer is C.

Two Containers of Equal Volume Are Connected by a Stopcock