Physics Olympiad question

Question

A small house is being heated by an electric heater of power P = 1 kW which maintains the interior temperature t₁ = 19℃; the outside temperature t₀ = 0℃. A man enters the house, upon which the room temperature starts rising and achieves a new value t₂ = 20℃. Find the “heating power” of the man.

Answer 1

Initial condition

The heater power is maintaining the house at a constant temperature of 19°C.

This power compensates for the heat lost due to the temperature difference between the inside (19°C) and the outside (0°C).

After the man enters

The new equilibrium temperature is 20°C. Let's assume the heating power of the man is P_man

Since the heat loss is proportional to the temperature difference between the inside and outside, we can set up the following relationship:

P_total/T_total=P_initialr/T_initial

where:

Using the proportionality:

(P_heater+ P_man)/20 = (P_heater)/19

Run the equation with: 

P_heater = 1000W

we find that P_man= 52.63W

Thus, the heating power of the man is approximately 52.63 W