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?

 

[rezeew]

I would approach this question by considering the principles of thermodynamics and heat transfer. The power supplied to the heater is converted into heat energy, which then transfers to the surrounding air in the room. This heat energy raises the temperature of the air, leading to a warmer room.

Based on this understanding, I would expect the relationship between power and temperature to be proportional, as you suggested. This means that as the power supplied to the heater increases, the temperature of the room will also increase. However, the rate at which the temperature increases may not be constant and could depend on factors such as the size of the room, insulation, and ventilation.

To determine the exact relationship between power and temperature, we would need to conduct experiments and collect data to plot a graph. This graph would likely show a positive correlation between power and temperature, with a steeper slope at lower power levels and a shallower slope at higher power levels. This is because as the room temperature increases, the rate of heat transfer also increases, making it harder for the heater to raise the temperature even further.

In summary, the relationship between power and temperature in a room is likely to be proportional, but the exact shape of the graph will depend on various factors and would require experimentation to determine.