An auditorium of size 40m x 20m x 8m has 600 people init. The temperature of the air is 27oC. It takes 29 Joule of thermal energy to raise the temperature of 1 mol of air by 1 K and the molar mass of air is 29 g/mol. Take the density of air to be constant at 1.25 kg/m3.
a) Obtain how many moles of air are there in auditorium?
b) Assuming that each person gives off thermal energy at a rate of 80 W, determine how fast the temperature in the auditorium is rising. Assume that the auditorium is closed so that cooler air does not enter.