Solving for the Temperature of an Outer Space Station Wall

[mizzy]

Homework Statement

A space station in outer space has a total surface area of 580m^2 with emissivity of 0.62. The temperature of the outside surface is 156K. The walls are 0.25m thick with an average thermal conductivity of 0.038W/mK. Find the temperature of the inner wall of the space station, assuming that the outside surface radiates into an environmnt that is very cold - essentially at 0.0K.

Homework Equations

P = kA(delta T)/L

P = stefan Boltzmann constant * A * emissivity * T^4

The Attempt at a Solution

No clue how to start. Can someone lead me to the right direction?

 

[6Stang7]

What is the heat sink for the interior of the ship? What about for the exterior surface of the ship? Look at this in terms of energy.

 

[mizzy]

What is the heat sink for the interior of the ship? What about for the exterior surface of the ship? Look at this in terms of energy.

what do you mean by heat sink??

 

[6Stang7]

Imagine you have a wall that has an interior temperature T_i and the outside surface temperature T_s such that T_i>T_s. In this case, the outside of the wall is acting as a heat sink; thermal energy is flowing from the source (T_i) to the sink (T_s). Apply this concept to the two sub-systems in your problem; the ship's hull and the surface of the ship's hull and space.

 

[mizzy]

Do I have to use heat conduction and radiation?

what would i use first? I'm looking for the inside temperature, so should i use the first equation?

 

[6Stang7]

Write the equations that you think are relevant and look at your knowns and unknows. How are the two types of thermal energy flow related?

 

[mizzy]

FOr the first equation, we are given k, thermal conductivity, A, area, L, thickness, and Ts is given. Don't know Ti.

FOr the second equation, we are given emissivity, we know stefan's constant, we know A, but I'm not sure about T. Is that the outer temperature that they gave?? 0.0K?

 

[6Stang7]

OK, so you know the first problem is a heat conduction problem.

The second problem is a radiation problem; now let's go a little deeper. What is emissivity? Why do you think T would be 0.0k?

How does the first equation relate to the second equation (hint: First Law of Thermodynamics).

 

[mizzy]

T would be 0.0K because it's the temperature of the surroundings. Emissivity is a constant telling you if they are good or poor emitters.

 

[6Stang7]

If T was 0.0k, what value would that give you for your equation?

Emissivity is a constant telling you if they are good or poor emitters.

Yes. More specifically, it is the ratio of the of the radiation emitted by the surface at the given temperature to the radiation emitted by a blackbody (a perfect emitter) at the same temperature.

Does this help you understand what the value of T?

 

[mizzy]

FOr the equation,the total power radiated is zero. correct?? so all i have to find is the inside temperature from the heat conduction equation.

 

[6Stang7]

If you say T=0.0K, then yes, the power of radiation is 0. However, is that true? If not energy is being lost to radiation, is there any heat flow? Read the definition of emissivity again. What temperature is it referring to?

 

[mizzy]

emissivity depends upon the nature and state of the surface. There is heat flow! in the question it says that the outside surface radiates into the environment. the temperature they are referring to is the difference in temperature from the heat conduction problem. First i have to find the internal temperature and then use the difference for the radiation problem??

 

[6Stang7]

So we know there is heat flow. So you have two sub-systems making up this problem; conduction through the wall and radiation from the outside surface of the wall into space.

How does the energy flow in the conduction problem compare to the energy flow in the radiation problem?

How many unknowns do you have in the conduction problem? How many unknowns do you have in the radiation problem?

 

[mizzy]

one unknown in the conduction problem, one unknown in the radiation problem.

you're losing energy in the conduction problem and gaining energy in the radiation problem. so therefore, lost of energy = energy gain? not sure...=( thermal physics is my weakness!

 

[mizzy]

wait a minute...for the heat conduction problem, inside temperature and power are unknowns. is that right? ok i think I'm confused again

 

[mizzy]

ok ok...i thought about it. The temperature in the radiation problem is the temperature of the outside surface of the space ship. I plug that into the radiation equation and get a radiated power. Then i should plug that in the heat conduction equation and then finally solve for the inside temperature.

am i correct?

 

[6Stang7]

Bingo!

You know that, for a steady-state system (which we assume this to be), the the amount of heat flow through the wall is the same amount of flow flow due to radiation.

 

[mizzy]

Bingo!

You know that, for a steady-state system (which we assume this to be), the the amount of heat flow through the wall is the same amount of flow flow due to radiation.

Thanks a lot for your help!