A group of 35 students attend a class in an insulated room which measures 11 by 8 by 3 m....

A group of 35 students attend a class in an insulated room which measures 11 by 8 by 3 m. Each student takes up about 0.075 m³ and gives out about 80 W of heat (1 W = 1 J/s). Calculate the air temperature rise during the first 20 minutes of the class if the room is completely sealed and insulated. Assume the heat capacity C_υ for air is 0.718 kJ/(kg K). Assume air is an ideal gas at 20 °C and 101.325 kPa. Note that the heat absorbed by the air Q is related to the mass of the air m the heat capacity, and the change in temperature by the following relationship:

The mass of air can be obtained from the ideal gas law:

where P is the gas pressure, V is the volume of the gas, Mwt is the molecular weight of the gas (for air, 28.97 kg/kmol), and R is the ideal gas constant [8.314 kPa m³/(kmol K)].