The rate of heat transfer to the surroundings from a person at rest is about 400

Question

The rate of heat transfer to the surroundings from a person at rest is about 400 kJ per hour. Suppose that the ventilation system fails in an auditorium containing 2000 people.
(a) How much does the internal energy of the air in the auditorium increases during the first 20 minutes after the ventilation system fails?
(b) Considering the auditorium and all the people as a system, and assuming no heat transfer to the surroundings, how much does the internal energy of the system change? How do you explain the fact that the temperature of the air increases?

Explanation / Answer

a)400 kJ energy inc per person per hour

=> per minute its 400/60 = 20/3 kJ

Heat given out by people will increase the internal energy of the people

=> for 2000 persons, rise in int energy of auditorium = 2000 * 20/3 = 13333.3 kJ

b) If both are considered as a system, with no heat trasnfer, the internal energy of sustem is CONSTANT

E = Q + W, both of which are zero in this case.

The air temp rises because of transfer of heat from people to air. However heat loss from the people makes their own body temps fall

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