Heat transfer and heat from lightbulbs

[tiffanysnow]

Homework Statement

Two rooms, each a cube 4.0m on a side, sare a 12cm thick brick wall. Because of a number of 100-W light-bulbs in one room the air is at 30 Celsius, while in the other room it is at 10 Celsius. How many of the 100-W light-bulbs are needed to maintain the temperature difference across the wall?

Homework Equations

I'm not so sure if this equation would work. But I have tried using it.
ΔQ/Δt = (kA(T-T))/l

The Attempt at a Solution

I used the above equation and got 213.3 J/s. But I do not know if I am going the rigt direction. The answer that the book gave is 22 bulbs. Please help me and explain how I can solve this.

 

[rl.bhat]

To solve the problem, the value of k is needed.

 

[tiffanysnow]

The value of k (for wood) = 0.08 to 0.16
The value of k (for air) = 0.023 J/s*m*C
What I have so far is (but I don't so if it is correct or not). This is the rate of heat flow
[(0.03J/s*m*C)(16m^2)(30C-10C)]/(0.12) = 213.3 J/s
But what do I do next or is this incorrect?

 

[kuruman]

The value of k (for wood) = 0.08 to 0.16
The value of k (for air) = 0.023 J/s*m*C
What I have so far is (but I don't so if it is correct or not). This is the rate of heat flow
[(0.03J/s*m*C)(16m^2)(30C-10C)]/(0.12) = 213.3 J/s
But what do I do next or is this incorrect?

The expression is correct, but the numbers in it are not. What does 0.03 J/s*m*C represent? It should be the thermal conductivity of wood. The assumption here is that the entire "hot" room is at 30 ^oC, so we do not have to worry about the conductivity of the air. To get the book's answer, you need to use the lowest of the values for wood (0.08). This will give you the minimum number of light bulbs required to do the job.

 

[rl.bhat]

The value of k (for wood) = 0.08 to 0.16
The value of k (for air) = 0.023 J/s*m*C
What I have so far is (but I don't so if it is correct or not). This is the rate of heat flow
[(0.03J/s*m*C)(16m^2)(30C-10C)]/(0.12) = 213.3 J/s
But what do I do next or is this incorrect?

The walls of the room are made of brick, not of wood. The thermal conductivity of brick is more than wood. Find k for brick.

 

[tiffanysnow]

The k value of brick is 0.84J/s*m*C.

 

[Redbelly98]

Good. Repeat your calculation from Post #3, using k for brick.

 

[yunie]

The expression is correct, but the numbers in it are not. What does 0.03 J/s*m*C represent? It should be the thermal conductivity of wood. The assumption here is that the entire "hot" room is at 30 ^oC, so we do not have to worry about the conductivity of the air. To get the book's answer, you need to use the lowest of the values for wood (0.08). This will give you the minimum number of light bulbs required to do the job.

I haven't really get what this post mean. How do we get the relationship between the no of bulb required and the rate of heat transfer? @_@

 

[Redbelly98]

Welcome to Physics Forums.

I haven't really get what this post mean. How do we get the relationship between the no of bulb required and the rate of heat transfer? @_@

Each bulb generates 100 Watts of heat. So, just for example, if the required rate of heat transfer turned out to be 300 Watts, how many bulbs would it take to generate that 300 W?