Heat capacity and temperature problem

[Krushnaraj Pandya]

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?

 

[gneill]

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.

 

[kuruman]

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 $P= dQ/dt$.

 

[Krushnaraj Pandya]

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?

 

[kuruman]

That looks correct.

 

[Krushnaraj Pandya]

That looks correct.

I got it, thank you very much :D