Hot Air in a Physics Lecture. (a) A typical student listening attentively to a physics lecture 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? (b) Assume that all the heat energy in part (a) is transferred to the 3200 m3 of air in the room. The air has specific heat 1020 J/kg · K and density 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? (c) 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?

Solution 97P Step 1 of 3: = 1.2 kg/m 3 3 v = 3200 m We know that = m v 3 3 m = v =1.2 kg/m × 3200 m = 3840 kg Step 2 of 3: a)We have equation Q = 3000 s × (90 students)(100 J/s) 7 = 2.7 × 10 J b)Q = mcT T = Q mc 2.7×10 = 3840×1020 = 6.89 C