# Heat transfer problem

1. Nov 18, 2013

### Saitama

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
I am not sure about the relevant equations to be used here. At first sight, I thought I had to apply Stefan's law but then, the question states the power consumed by bulb, not the radiated one. I am completely clueless about what to do here. The first line states the peak wavelength, I have seen peak wavelength being used in Wien's displacement law but I am not sure about this.

Any help is appreciated. Thanks!

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2. Nov 18, 2013

### haruspex

You know the power going into the bulb. How does that relate to the power coming out of the bulb?
Can you determine the temperature? What then does Stefan's Law tell you?

3. Nov 18, 2013

### Saitama

Yes, its 60 watts (0.5*120)

And that's where I am stuck. Can you please give me some hints?
Temperature of bulb? How?

4. Nov 18, 2013

### SteamKing

Staff Emeritus
5. Nov 18, 2013

### Saitama

Ah yes, so the temperature of bulb is $2.898 \times 10^3 K$.

What next?

From Stefan's law,

$$P_e-P_a=\sigma A(T_e^4-T_a^4)$$

where $P_e$ is the rate at which heat energy is emitted, $P_a$ is the rate at which heat energy is absorbed. $T_e$ is the temperature of body and $T_a$ is temperature of air.

Now how do I find $P_e$ and $P_a$?

6. Nov 18, 2013

### SteamKing

Staff Emeritus
I think for your light bulb, Pa = 0 and you are given the information on the power consumption of the bulb in the OP. I say Pa = 0 because the energy input to the bulb is converted to light, and air is transparent to light (i.e., light radiates without being absorbed by the air).

7. Nov 18, 2013

### Saitama

Something like $60=\sigma A((2.8998 \times 10^3)^4-(300)^4)$, right?

8. Nov 18, 2013

### SteamKing

Staff Emeritus
That would be my guess. You know the Boltzmann constant σ (or can look it up.)

9. Nov 18, 2013

### Saitama

Thanks a lot SteamKing! That's the correct answer. :)

But I feel that the question didn't give enough information. Don't you think the problem should have specified the nature of bulb? I mean I had to consider it as a black body to reach the correct answer.

10. Nov 18, 2013

### SteamKing

Staff Emeritus
I'm not sure what you mean by 'the nature of the bulb.'

Hot objects radiate energy as a black body at a certain temperature. The only thing missing that I can see was the emissivity value of the filament. Since, for this problem, the emissivity was apparently assumed to be 1, then you are dealing with a perfect black body radiator.

11. Nov 18, 2013

### haruspex

I agree the emissivity should be taken as 1 here, in the absence of any other indication, but in general objects can radiate better at specific wavelengths. A filament of a different metal would have a different colour at the same temperature.