Classical thermodynamics problem

[spaghetti3451]

Homework Statement

(i) State the Second Law of Thermodynamics in one or other of its forms.

(ii) The heat capacity per unit volume of a particular solid at low temperatures is equal to CT³; find expressions for its internal energy and entropy S per unit volume (ignoring the effects of thermal expansion).

Homework Equations

The Attempt at a Solution

(i) Kelvin's statement: No process is possible whose sole effect is complete conversion of heat into work.

Clausius' statement: No process is possible whose sole effect is to transfer heat from a colder to a hotter body.

(ii) Not sure. Any help would be awesome.

 

[darkxponent]

Atleast show us the attempt

 

[spaghetti3451]

Heat capacity = Internal energy/ Temperature, so Internal energy = CT⁴. Now, I know that this is wrong, but that's the point of me coming to the forum, so I can get the problem done quickly. Otherwise I can just read the lecture notes and get the problem done in 60 long and boring minutes, which isn't fun becasue I am a third year student and I am studying this for the comprehensive paper and if I take this long to do one problem, then i will take eternity to finish all the first and second year courses and so I might as well pack my bag and run for home.