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Thread: Heat radiation problem

  1. #1 Heat radiation problem 
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    The question is as follows:

    A radiating body has a Kelvin temperature , and its surroundings are at 500K (T0 >500K). If the Kelvin temperature of the radiating body is increased to 5T0, the net rate at which the body radiates increases by a factor of 14. What was the original temperature T0?

    Attempt at a solution:

    Using P=EPSILON*DELTA*A*(T0^4-TS^4) where T0 is temperature of the body and TS is temperature of the surroundings (i.e. 500K).

    Epsilon (emmisivity), Delta (Stefan–Boltzmann constant) and A (area) can all be considered constants as they are intrinsic properties of the body which do not change.

    I then called these constants a new constant B.

    My two equations are now:

    P=B(T0^4-TS^4)
    14P=B(5T0^4-TS^4)

    Isolating B in each equation and equating gives:

    P/(T0^4-TS^4)=14P/(5T0^4-TS^4)

    Subbing in the value for TS = 500K and working out the value for T0 keeps giving me an incorrect answer.

    Most times I get an answer <500K and the only thing I got >500K was around 568K or so and this was incorrect (I have to submit online).

    Any help would be appreciated.

    Thanks


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  3. #2  
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    Are you raising the 5 to the fourth power, or just multiplying T0^4 by 5?


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  4. #3  
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    Raising 5 to the 4th power sorry it wasn't clear.
    Thinking of the question is greater than knowing the answer...
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  5. #4 Re: Heat radiation problem 
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    Quote Originally Posted by Mars
    Isolating B in each equation and equating gives:

    P/(T0^4-TS^4)=14P/(5T0^4-TS^4)

    Subbing in the value for TS = 500K and working out the value for T0 keeps giving me an incorrect answer.

    Most times I get an answer <500K and the only thing I got >500K was around 568K or so and this was incorrect (I have to submit online).

    Any help would be appreciated.

    Thanks
    Your equation



    is correct.

    If subbing in the value for TS = 500K and working out the value for T0 keeps gives you an incorrect answer, the there is something wrong with how you are solving the equation.











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  6. #5  
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    It's telling me that this answer (548) is incorrect. Does the fact that the question states the *NET* rate of radiation increases by a factor of 14 have any significance?
    Thinking of the question is greater than knowing the answer...
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  7. #6  
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    Quote Originally Posted by Mars
    It's telling me that this answer (548) is incorrect. Does the fact that the question states the *NET* rate of radiation increases by a factor of 14 have any significance?
    Maybe, but that terminology doesn't mean anything to me. It sounds like whoever formulated the question is a bit sloppy and has his own terminology.

    He might mean net heat flow rather than radiation.

    Or perhaps he screwed up the answer.
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  8. #7  
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    As Harold pointed out, you also have to raise the 5 to the 4th power. Where you have 5T^4 you should have 625T^4.

    However I think the problem statement as written is impossible. The heat radiated is going to asymptote toward the ratio of temperatures to the 4th power. For a 14 fold increase in radiation the temperature ratio has to be approximately 1.934. As radiating temperature increases the surroundings temperature becomes increasingly less important.
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  9. #8 Re: Heat radiation problem 
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    Quote Originally Posted by Mars
    Isolating B in each equation and equating gives:

    P/(T0^4-TS^4)=14P/(5T0^4-TS^4)

    Subbing in the value for TS = 500K and working out the value for T0 keeps giving me an incorrect answer.

    Most times I get an answer <500K and the only thing I got >500K was around 568K or so and this was incorrect (I have to submit online).

    Any help would be appreciated.

    Thanks
    The comment of Harold and Bunbury is right. Unfortunately it does not lead to a clean solution.

    Your equation



    should be




    So,.











    which is quite impossible.
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