Examstyle Questions: Kinetic Theory

A gas cylinder with a volume of 0.1 m^{3} contains Helium at a temperature of 300 K. The pressure of the helium is 1.1 x 10^{5} Pa. Calculate:
a) The mass of helium in the cylinder
(4 Marks)
b) The r.m.s. speed of the helium atoms.
(3 Marks)
(Marks available: 7)

A cylinder contans 0.005 m^{3 }of a gas at 20°C and at constant pressure of 100 K Pa. The gas is heated and it pushes back a piston at the end of the cylinder by 20 mm and increases its volume. The pressure of the gas remains unchanged.
a) What force does the gas exert at the piston of its area is 1.5 x 10^{2} m^{2}.
(2 Marks)
b) How much work is done by the gas as it expands.
(3 Marks)
c) What is the final temperature after the gas has expanded? (The mass of gas and its pressure do not change).
(3 Marks)
(Marks available: 8)
Answer outline and marking scheme for question:

a)
(4 Marks)
b)
(3 Marks)
(Marks available: 6)

a) F = p x A (1 Mark) = 100 x 10^{3 }x 1.5 x 10^{2}
= 1.5 x 10^{3} N OR 1.5 kN (1 Mark)
(2 Marks)
b) W = pΔV (1 Mark) ; ΔV = A Δx = 1.5 x 10^{2} x 2 x 10^{2}
ΔV = 3 x 10^{4} m ^{3} (1 Mark)
So, W = 100 x 10^{3} x 3 x 10^{4}
W = 30J (1 Mark)
(3 Marks)
c)
(3 Marks)
(Marks available: 8)