On a cold day you inhale 14 L of air at 20 C and its tempera

On a cold day you inhale 1.4 L of air at -20 C and its temperature is raised to 40C. Assume that you can treat the air as a diatomic ideal gas with a pressure of 1.0 atm. What is the total change in kinetic energy of the air you inhaled?

Solution

average KE of a molecule = 3 kT / 2

using PV = nRT

(1 x 101325 Pa x 1.4 x 10^-3 m^3 ) = n x 8.314 x (273 -20)

n = 0.067 moles

so no. of molecule = 0.067 x 6.022 x 10^23 = 0.406 x 10^23 molecules

initial KE per molecule = (3 x 0.406 x 10^23 x 1.38 x 10^-23 x (273-20)) /2 = 212.69 J

final KE = (3 x 0.406 x 10^23 x 1.38 x 10^-23 x (273+40))/2 = 263.13 J

change in KE = 50.44 J