A room of10 m xx 15m xx4m dimenstion having perfectly insulated walls, ceiling and floor has 60 students seated inside. The air inside the room is at 25^(@)C and 1 atm pressure. If each student loses 200 joules of heat in one second, calculate the rise in temperature noticedin 20 minutes ( Neglect loss of air to the outside as temperature is raised and C_(p) for air = ( 7)/( 2) R).

A room of10 m xx 15m xx4m dimenstion having perfectly insulated walls,

1.	A room of10 m xx 15m xx4m dimenstion having perfectly insulated walls, ceiling and floor has 60 students seated inside. The air inside the room is at 25^(@)C and 1 atm pressure. If each student loses 200 joules of heat in one second, calculate the rise in temperature noticedin 20 minutes ( Neglect loss of air to the outside as temperature is raised and C_(p) for air = ( 7)/( 2) R).
Answer» Solution :Volume of room `= 10 m XX 15m xx4m = 600m^(3)= 600 xx 10^(3) L =6 xx 10^(5) L` Molesof air in the room at `25^(@)C` at 1 atm pressure `n = ( PV)/( RT) = ( 1 xx 6 xx 10^(5))/( 0.0821 xx 298) = 2.45 xx 10^(4)` Heat producedin1 sec by each student `= 200 J` `:. `Heat produced in 1 sec by 60 students `= 200 xx 60 J = 12000J` Heat produced in 20 minutes `=12000 xx 20 xx60 J = 144 xx 10^(5)J` Change in enthalpy of air, `DELTA H = n C_(p) DeltaT` `:. 144 xx 10^(5) = ( 2.45 xx 10^(4)) = ( ( 7)/(2) xx 8.314)xx Delta T ` or ` Delta T = 20.2 K`