Three identical 10 L tanks contain 6 mol of helium (He) at 293 K. The pressure in each of the tanks is increased as described below: Tank A: The tank volume is decreased from 10 L to 5 L while the temperature and the number of moles of He remain constant. Tank B: The tank temperature is increased from 293 K to 308 K while the volume and the number of moles of He remain constant. Tank C: The number of moles of He in the tank is increased from 6 mol to 9 mol while the temperature and the volume remain constant. How is the average kinetic energy, KE, of the He molecules affected in each case?

Under the assumption of ideal gas behavior, the average kinetic energy (KE) of a gas depends exclusively on the the temperature of the gas. Acutally, the temperature of a gas is a measure of its average kinetic energy.

Then, to predict how is the average kinetic energy, KE, of the He molecules affected in each case, you have to find the effect of the change on the temperature of the gas.

Case 1. Tank A.

V₀ = 10 liter
n₀ = 6 moles
T₀ = 293 K

V₁ = 5 liter
T₁ = T₀ = 293 K
n₁ = n₀ = 6 moles

Since, the temperature remains constant, which, as stated, is the measure of the kinetic energy, the average kinetic energy, KE, of the He molecules does not change.

Case 2. Tank B.

V₀ = 10 liter
n₀ = 6 moles
T₀ = 293 K

V₁ = 10 liter
T₁ = T₀ = 308 K
n₁ = n₀ = 6 moles

Since, the temperature increases, which, as stated, is the measure of the kinetic energy, the average kinetic energy, KE, of the He molecules increases.

Case 3. Tank C

.

V₀ = 10 liter
n₀ = 6 moles
T₀ = 293 K

V₁ = 10 liter
T₁ = T₀ = 293 K
n₁ = n₀ = 9 moles

Since, the temperature increases, which, as stated, is the measure of the kinetic energy, the average kinetic energy, KE, of the He molecules increases.