Two tanks, both of volume 10 L, are connected by a valve and are thermally isolated. One tank contains 1mole of ⁴He at 280 K and the other tank contains 1 mole O₂ at 300 K. The valve is then opened and the gases allowed to mix. What is the final temperature after the gases have come to equilibrium? A) 290 K B) 295 K C) 285 K D) 293 K E) 287 K

Question

Quizplus · Accepted Answer

We can use the equation for the final temperature of two gases mixing at constant volume:

Tf = [(n1 * Cv1 * T1) + (n2 * Cv2 * T2)] / [(n1 * Cv1) + (n2 * Cv2)]

where n = number of moles, Cv = molar heat capacity at constant volume.

Plugging in the values:

Tf = [(1 * 5/2 * 280) + (1 * (5/2)*3/2 * 300)] / [(1 * 5/2) + (1 * 5/2 * 3/2)]
Tf = 293 K

Therefore, the final temperature is 293 K. Answer choice D is correct.

Two Tanks, Both of Volume 10 L, Are Connected by a Valve