Hard molar specific heat question?

[fantexihong]

Homework Statement

At very low temperatures, the molar specific heat of many substances varies as the cube of the absolute temperature: C=k*(T^3/To^3),
which is sometimes called Debye's law. For rock salt, To= 281K and k= 1940 J/mol*K

Determine the heat needed to raise 2.40 mol of salt from 30.0K to 50.0K .

Homework Equations

I don't know if this equation applies to solid . Q=nC*ΔT

The Attempt at a Solution

I know ΔT is 20, it seems to me that the only unknown for this question is T.
I tried to plug in 30 OR 50 into T, but I got the wrong answer.

 

[Borek]

Q=nCΔT is OK, but to make things more difficult C is a function of temperature.

 

[fantexihong]

Q=nCΔT is OK, but to make things more difficult C is a function of temperature.

Could you tell me how to get the C value for this question? I know C=k*(T^3/To^3) from the problem, it also gives me k and To value, but I don't know what is T value.

 

[Borek]

T is given in the problem and is not constant - it changes from 30 to 50 K. You need to integrate.

 

[fantexihong]

T is given in the problem and is not constant - it changes from 30 to 50 K. You need to integrate.

It works!I just need to integrate that C function, thank you!