Question

Consider a classroom that is roughly 5 m × 10m × 3m. Initially t = 27⁰C and P = 1 atm. There are 50 people in an insulated class loosing 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 42⁰C and person feels uncomfortable above this temperature. Heat capacity of air = (7/2) R.

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

Answer 1

Answer: (B)

5.91 minutes

Answer 2

Volume = 5 × 10 × 3 = 150m3 = 150 × 103 L ; T = 27⁰C = 300 K; P = 1 atm

PV = nRT $\Rightarrow$ 1 × 150 × 103 = n × 0.082 × 300 $\Rightarrow$ n = 6097.6

Total energy released per second = 150 ´ 50 = 7500 J/sec.

Amount of energy released by persons = energy gained by air $\Rightarrow$ [7500] tsec = n C[dT]

$\Rightarrow$ 7500 tsec = 6097.6 × $\frac{7}{2}$ × 8.312 × 15

$\Rightarrow$ tsec = 354.87 sec. =$\frac{354.87}{60}$= 5.91 minutes.