How does temperature vary with power in a room?

[baha]

Homework Statement

A typical room is heated with an electric heater on which the power (and thus heat output) can be varied. What do you think the relationship might be between the power supplied to the heater and the resulting warmer temperature the room reaches? Ie if you were to plot a graph of power vs temperature what would it look like? (assume that the radiator remains on at the chosen power and the temperature is recorded once the room has reached equilibrium)

Homework Equations

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The Attempt at a Solution

This is the bonus question of my homework and is not for credit, however I thought it was really interesting. From my own general experience at home, I would guess the graph would be simply a straight line proportional graph. What do you think?

 

[AlephZero]

I would guess the graph would be simply a straight line proportional graph

What do the axes of the graph measure? Hint: if the heater is always on, do you think the room temperature will be the same in summer and in winter?

 

[baha]

The y-axis would be in oC and would show the values for the maximum temperatures that the room reached at equilibrium and the x-axis would be the power.

 

[baha]

But is it directly proportional?