Find rate of temperature change using heat capacity, density and area

[JoeyBob]

Homework Statement

see attached

Relevant Equations

dQ/dt=Ae*5.67E-8*T^4

So first I found rate of heat change using the above equation, with T=883K, e=1, SA= 6*l^2=21.66

Now dQ/dt=746593.71 W

Now I am not sure entirely what to do next. They give density so I likely have to get the mass from that, M=pV,=1.9^3*4037=27689.783 kg.

My issue is that I don't know how to relate change in heat to h=change in temperature.

I could try Q=mc(change in T). But I have change in Q, not Q. Not sure how I would integrate dQ/dT either...

Answer is -0.04121 btw.

 

[hutchphd]

What is the definition of specific heat capacity? Might be relevant...

 

[TSny]

I could try Q=mc(change in T). But I have change in Q, not Q.

You have Q = mcΔT. Let Δt be the time interval corresponding to the change in temperature ΔT. Think about the equation that you get by dividing both sides of Q = mcΔT by Δt. For small Δt, how does the left side relate to dQ/dt?

 

[JoeyBob]

You have Q = mcΔT. Let Δt be the time interval corresponding to the change in temperature ΔT. Think about the equation that you get by dividing both sides of Q = mcΔT by Δt. For small Δt, how does the left side relate to dQ/dt?

So I can find dQ/dt using dQ/dt=A*5.67E-8*T^4

I can find m using m=pV

And I know Q=mc(change in T)

But dQ/dt isn't Q. Or can I just put it in the equation anyways and solve for change in T and it will work?

 

[Chestermiller]

$$\frac{dQ}{dt}=mc\frac{dT}{dt}$$