Question

Consider a classroom that is roughly $5m\times 10m\times 3m.$ Initially $T={27}^{\circ }C$ and $P=1atm$. There are $50$ people in an insulated class losing energy to the room at the average rate of $150watt$ per person. How long can they remain in class if the body temperature is ${42}^{o}C$ and the person feels uncomfortable above this temperature?

[Molar heat capacity of air = $\left(7/2\right)R$]

• A. 4.34 minutes
• B. 5.73 minutes
• C. 6.86 minutes
• D. 7.79 minutes

Answer 1

The correct option is B 5.73 minutes

Given:
Volume of room $V=5\times 10\times 3\times {10}^3$ lit

$P=1atm,R=0.082atmLmo{l}^{-1}{K}^{-1},T=30+273=303K$

no. of moles of air $n=\frac{PV}{RT}=6.1\times {10}^3$

Heat produced per second by '50' students

$=50\times 150=7500Watt/sec$

$\Delta H_{air}=n{C}_P.\Delta T$

$7500\times t\times 60=6.1\times {10}^3\times 7/2\times 8.314\times 15$

$t\approx 5.73$ minutes