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Heat capacity and temperature problem

  • #1
Krushnaraj Pandya
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Homework Statement


A piece of metal is heated by supplying a constant power P. The temperature of the metal starts varying as T=kt. The heat capacity of the metal as a function of temperature is?

Homework Equations


Q=CdT

The Attempt at a Solution


From Q=CdT, dT is k, since P is Q/t, I plugged this into the equation but the answer is way off. Can someone explain what I'm missing?
 

Answers and Replies

  • #2
gneill
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Consider how you've defined power: P = Q/t. Is that correct? Generally we think of power as the rate of energy delivered or consumed per unit time.
 
  • #3
kuruman
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You are missing what you missed in your other post. Power is rate of change and involves a derivative not a ratio. Here, ##P=dQ/dt##. You need to consider that ##C=dQ/dT## and relate that to ##P= dQ/dt##.
 
  • #4
Krushnaraj Pandya
Gold Member
697
72
You are missing what you missed in your other post. Power is rate of change and involves a derivative not a ratio. Here, ##P=dQ/dt##. You need to consider that ##C=dQ/dT## and relate that to ##P= dQ/dt##.
oh ok, so P=dQ/dt and dQ=CdT, therefore Pdt=CdT, P=CdT/dt therefore P=Ck, is this correct?
 
  • #5
kuruman
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That looks correct.
 
  • #6
Krushnaraj Pandya
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That looks correct.
I got it, thank you very much :D
 

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