`50` students sitting in the room of `5 xx 10 xx 3m^(3)` dimensions. The air inside the room is at `27^(@)C` and `1atm` pressure. If each student loses `100` watt heat per second assuming the walls, ceiling floor, and all the material present inside the room is perfectly insulated as well as neglecting loss of air to the outside as the temperature is raised, how much rise in temperature will be noticed in `10min`? Given `C_(P) = (7)/(2)R` for air.

Explanation

Volume of the room `5 xx 10 xx3= 150 m^(3) = 15 xx 10^(4)L`
Moles of air in the room at `27^(@)C` and `1atmP`,
`n = (PV)/(RT) = (1xx15 xx 10^(4))/(0.0821xx300) = 6.1 xx 10^(3)`
Heat produced per second by `50` students `= 100 xx 50`
`= 5000 W s^(-1)`
Heat produced in `10min = 5000 xx 10 xx 60W`
`= 3 xx 10^(6) W or J s^(-1)`
`:.` Change in enthalpy of air, `DeltaH = n xx C_(P) xx DeltaT`
`3 xx 10^(6) = 6.1 xx 10^(3) xx (7)/(2) xx 8.314 xx DeltaT rArr DeltaT = 16.90`
Thus, a rise of `16.90^(@)C` will be noticed in air tempertaure.