Consider a class room of dimensions 5 xx 10 xx 3 m^3at temperature 20^@C and pressure 1 atm. There are 50 peoples in the room, each losing energy at the average of 150 Joule/sec. Assuming that the walls ceiling, floor and furniture perfectly insulated and none of them absorbing heat, how much time will be needed for rising the temperature of air in the room to body temperature, i.e., 37^@C. For air C_p = 7/2 R . Loss of air to the outside as the temperature rise may be neglected.

Consider a class room of dimensions 5 xx 10 xx 3 m^3at temperature 20^

1.	Consider a class room of dimensions 5 xx 10 xx 3 m^3at temperature 20^@C and pressure 1 atm. There are 50 peoples in the room, each losing energy at the average of 150 Joule/sec. Assuming that the walls ceiling, floor and furniture perfectly insulated and none of them absorbing heat, how much time will be needed for rising the temperature of air in the room to body temperature, i.e., 37^@C. For air C_p = 7/2 R . Loss of air to the outside as the temperature rise may be neglected.
Answer» 502.3 SEC 411.3 sec 602.2 sec 702.4 sec Solution :Given P= 1ATM, T = 273 + 20 = 293 K Volume of air in the room ` = 5 xx 10 xx 3 m^3` ` = 150m^3 = 150 xx 10^6cm^3` As ` PV = nRT` ` therefore = n = (PV)/(RT) ` where n = moles of air `= (1 xx 150 xx 10^6)/(10^3 xx 0.0821 xx 293) = 6.236 xx10^3 , Delta H = n.C_P . Detla T` ` = 6.236 xx 10^3 xx 7/2 xx 8.314 xx (310 - 293) = 3.085 xx 10^6 J` Therefore , HEAT needed to heat the room to `37^@C` `= 3.085 xx 10^6 J` Also heat released by 50 people ` = 150 xx 50 J//sec = 7500 J//sec` `because` 7500 J heat is produced in 1 sec ` therefore 3.085 xx 106 J` heat will be produced in `(1 xx 3.085 xx 10^6)/(7500)` ` = 411.3 sec `