`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.

Options

A. `15.90^(@)C`
B. `16.90^(@)C`
C. `14.90^(@)C`
D. `17.90^(@)C`

Answer

B

Explanation

Vol. of room `1=5xx10xx3=150 m^(3)`
`=15xx10^(4) litre`
Moles of air in the room at `27^(@)C` and `1 atm P`
`n=(PV)/(RT)=(1xx15xx10^(4))/(0.0821xx300)=6.1xx10^(3)`
Heat produced by `50` student `=100xx50`
`5000` watt `sec^(-1)`
Heat produced in `10` minutes `=500xx10xx60`
`=3xx10^(6)` watt `sec^(-1)` or `Jsec^(-1)`
`:.` change in enthalpy of air, `DeltaH=nC_(p)xxDeltaT`
`3xx10^(6)=6.1xx10^(3)xx7/2xx8.314xxDeltaT`
`:. DeltaT=16.90^(@)`