Specific heat capacity varies with temperature.

[necromanzer52]

Homework Statement

Heating a .8 kg disk of iron from 20 C to 400 C, but the specific heat capacity changes from 456 at 20 C, to 615 at 400 C. It hints that I'm supposed to find the average to solve the equation.

Homework Equations

E = mC(dT)

The Attempt at a Solution

I have a strong feeling, that I'm supposed to use calculus to solve this, but I can't think of any equations to differentiate, or how it would be, in any way, useful.

I've also thought about plotting the specific heat capacity against kelvin, and using the specific heat capacity at the midpoint (483.15k)

 

[Acut]

Just a hint

dE = m d(CT)
dE = m (CdT + TdC) (product rule)

Integrate both sides and find the answer.