A cylinder with a piston contains 2.00 liters of an ideal diatomic gas at 1.00 atm and 275 K.The gas is subject to an adiabatic compression from its initial volume to 1/4 its initial volume.What is the temperature after the compression?

Question

Quizplus · Accepted Answer

Since the process is adiabatic, we have:

PV^γ = constant

where P is pressure, V is volume, and γ is the ratio of specific heats (Cp/Cv) for a diatomic gas, which is 1.4.

We can use this equation to find the final temperature after the compression:

P1V1^γ = P2V2^γ

T2 = T1 * (V1/V2)^(γ-1)

We're given that V2 = V1/4, so V1/V2 = 4. Plugging in the values:

T2 = 275 K * 4^(1.4-1)

T2 = 692.9 K

Rounding to two significant figures, the answer is B) 693 K.

A Cylinder with a Piston Contains 2