Question

1. A typical student listening attentively to a physics lecture class has a heat output of 100 W. How much heat energy does a class of 90 physics students release into a lecture hall over the course of a 50-min lecture?
2. Assume that all the heat energy in part 1 is transferred to the 3200 m³ of air in the room. The air has a specific heat capacity of 1020 J/kg-K and a density of 1.20 kg/m³. If none of the heat escapes and the air conditioning system is off, how much will the temperature of the air in the room rise during the 50-min lecture?
3. If the class is taking an exam, the heat output per student rises to 280 W. What is the temperature rise during 50 min in this case?

Answer 1

1.

$$90\times100 \frac {J}{s}\times3\times 10^3s=2.7\times 10^7 J$$

2.

$$\varDelta t=\frac {Q}{cm}$$

$$\varDelta t=\frac {2.7\times 10^7 J}{1020\frac {J}{kg-K} \times 1.2 \frac {kg}{m^3}\times 3200 m^3}=6.9 K$$

3.

$$90\times280 \frac {J}{s}\times3\times 10^3s=7.56\times 10^7 J$$

$$\varDelta t=\frac {7.56\times 10^7 J}{1020\frac {J}{kg-K} \times 1.2 \frac {kg}{m^3}\times 3200 m^3}=19.3 K$$