kinetic energy of ideal gas

A 1.1mol sample of hydrogen gas has a temperature of 24 degree C. What is the total kinetic of all the gas molecules in the sample?
(The temperature should be 224°C instead of 24°C . Otherwise, the answer would be 4100 J.)

Number of moles, n = 1.1 mol
Absolute temperature, T = (273 + 224) K = 497 K
Gas constant = 8.314 J/(mol K)

Kinetic energy, Ek
= (3/2)nRT
= (3/2) x 1.1 x 8.314 x 497 J
= 6800 J (2 sig. fig.)


How fast would a 65-kg person have to run to have the same kinetic energy?

Ek = 6800 J
m = 65 kg

Ek = (1/2)mv^2
v^2 = 2Ek/m
v = √(2Ek/m)

Speed, v
= √(2 x 6800/65) m/s
= 14 m/s (2 sig. fig.)