A cylinder with a frictionless movable piston contains an ideal gas at 400K. After the temperature of the cylinder is increased to 800K at constant barometric pressure

Question

A cylinder with a frictionless movable piston contains an ideal gas at 400K. After the temperature of the cylinder is increased to 800K at constant barometric pressure, which of the following will NOT be true?

a) the volume of the gas in the cylinder at 800K will be twice the volume of the gas in the cylinder at 400K

b) the average kinetic energy of the gas in the cylinder at 800K will be at 400K

c) the frequency and force of the gas particle collisions in the cylinder at 800K will be greater than they were at 400K

d) the root-mean-square velocity of the gas in the cylinder at 800K will be greater than what it was at 400K

e) the pressure of the gas inside the cylinder at 800K will be twice the pressure of the gas in the cylinder at 400K.

Please provide an explanation to the answer. Thanks in advance.

Answer 1

Constant pressure - Charles Law:

V1/T1 = V2/T2

V2 = V1T2/T1 = V1(T2/T1) so if T2 is 2x T1 (i.e. temp doubles), then volume is double also (V2 = 2xV1), so

(a) is true.

(b) doesn't make sense. The average kinetic energy at 800K will be greater than that at 400K

(c) this is true because as temp increases particles move faster and collisions/unit time increase

(d) this is true since rms = √3RT/M so as Temp increases so does rms velocity

(e) false. Since the piston is frictionless and the atmospheric pressure is constant, the volume of gas in the cylinder will increase and the pressure will remain constant.