# Heat capacity and temperature problem

Gold Member

## 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?

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
Mentor
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
Homework Helper
Gold Member
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##.

Gold Member
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
Homework Helper
Gold Member
That looks correct.

Gold Member
That looks correct.
I got it, thank you very much :D