# How does temperature vary with power in a room?

• baha
In summary, the graph of power vs temperature for a room heated with an electric heater is likely to be a straight line, with the power on the x-axis and the maximum temperature reached at equilibrium on the y-axis. This suggests that the relationship between power supplied and temperature is directly proportional. However, it is important to consider external factors such as seasonal changes which may affect the temperature despite the chosen power level.
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)

?

## 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?

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?

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.

But is it directly proportional?

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.

## 1. How does temperature vary with power in a room?

The temperature in a room can vary with the power used in the room. This is because the power used can affect the heating or cooling mechanisms in the room, which can ultimately impact the temperature.

## 2. What factors influence the temperature changes in a room with power usage?

There are several factors that can influence the temperature changes in a room with power usage. These include the type of heating or cooling system, the insulation of the room, the size of the room, and the outside temperature.

## 3. Is there a direct relationship between power and temperature in a room?

Yes, there is a direct relationship between power and temperature in a room. As the power usage increases, the temperature in the room will also increase. Similarly, as the power usage decreases, the temperature in the room will also decrease.

## 4. Can the temperature in a room be controlled by adjusting the power usage?

Yes, the temperature in a room can be controlled by adjusting the power usage. This is why many buildings have thermostats that allow the occupants to adjust the power and ultimately control the temperature in the room.

## 5. How can one maintain a consistent temperature in a room with varying power usage?

To maintain a consistent temperature in a room with varying power usage, it is important to have a properly functioning heating and cooling system, good insulation, and to monitor and adjust the power usage as needed. It is also helpful to keep doors and windows closed to prevent outside temperature fluctuations from affecting the room's temperature.

Replies
22
Views
2K
Replies
1
Views
1K
Replies
34
Views
2K
Replies
8
Views
2K
Replies
25
Views
3K
Replies
3
Views
2K
Replies
14
Views
1K
Replies
1
Views
953
Replies
106
Views
2K
Replies
15
Views
2K