What is the total (including rotational) thermal energy of the air in your lungs

Question

What is the total (including rotational) thermal energy of the air in your lungs? Assume that the total volume of your lungs is 2.1 liters, that your body temperature is 312 K, that the pressure is 1 atmosphere, and that all the molecules are diatomic. What is the typical speed of one of the nitrogen molecules in your lungs? Here we define the typical speed as the root-mean-square velocity. v_rms = What is the thermal energy of a penny at a temperature of 305 K? The penny weighs 1 gram and is composed mainly of copper, which has an atomic weight of 63 g/mol. U = From what height would a penny have to be dropped in order to gain a center-of-mass energy equal to its thermal energy, as calculated above? h = What is its final speed? v_cm =

Explanation / Answer

1)

U = 5/2 * nRT

by ideal gas PV = nRT

U = 5PV/2

U = 5.25 J

2 )

Vrms = sqrt(3RT/M)

M = 28 g/mol = 28 x 10^-3 kg/mol

R = 8.314

T = 312K

vrms = 527.19 m/s

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