Consider a classroom that is roughly `5mxx10mxx3m`. Initially `T=27^(@)`C and p=1 atm. There are 50 people in a insulated class losing energy to the room at the average rate of 150 Watt per person. How long can they remain in class if the body temperature is `42^(@)` C and person feels uncomfortable above this temperature. Heat capacity of air=`(7//2)R`

Options

A. 4.34
B. 5.91
C. 6.86
D. 7.79

Answer

B

Explanation

Volume of room `= 5 xx 10 xx 15 xx 10^(4)` lit
no of moles of air `= (P_(V))/(RT) = 6.1 xx 10^(3)`
Heat produced per second by '50' students `= 50 xx 150 = 7500` Watt/sec
`Delta H_("air") = n C_(P). Delta T`
`1500 xx t xx 60 = 6.1 xx 10^(3) xx (7)/(2) xx 8.314 xx 15`