`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 air in the room `= 5 xx 10 xx 3`
`= 150 m^(3) = 150 xx 10^(6) cm^(3)`
`:.` Mole of air `=n = (PV)/(RT) = (1xx150xx10^(6))/(10^(3) xx 0.0821xx293) = 6.236 xx 10^(3)`
`rArr C_(P) = (DeltaH)/(DeltaT)` (for `1` mole)
`:. DeltaH = n.C_(P).DeltaT` (for `n` mole)
`= 6.236 xx 10^(3) xx (7)/(2) xx 8.314 xx (310 - 293)`
`= 3.085 xx 10^(6) J`
Thus, heat needed to heat the room to `37^(@)C = 3.085 xx 10^(6)J`
Also, heat released by `20` peoples `= 3000 J s^(-1) = 150 xx 30`
`= 3000 Js^(-1)`
`3000 J` is provided in `1 s`.
`:. 3.085 xx 10^(6)J` heat will be provided in
`= (1 xx3.085xx10^(6))/(3000) = 1028.35s`