How do I solve for C in this entropy equation?

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Homework Statement


Basically I'm given Cv = aT + bT3 when T<50K and where Cv is the heat capacity of one mole of Aluminum and I'm asked to find an equation for the entropy as a function of T.

Homework Equations


dS = Cv/T dt

The Attempt at a Solution



So I integrated the above equation and got S = aT + bT3/3 + C and now I am just wondering how exactly am I supposed to solve for C? I'm not given any other information so should I just drop the constant of integration? I have a feeling I'm just missing something very simple though.
 
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jason177 said:

Homework Statement


Basically I'm given Cv = aT + bT3 when T<50K and where Cv is the heat capacity of one mole of Aluminum and I'm asked to find an equation for the entropy as a function of T.

Homework Equations


dS = Cv/T dt

The Attempt at a Solution



So I integrated the above equation and got S = aT + bT3/3 + C and now I am just wondering how exactly am I supposed to solve for C? I'm not given any other information so should I just drop the constant of integration? I have a feeling I'm just missing something very simple though.
All you need to do is define S as the integral for certain limits of integration. According to the question, the equation for Cv applies when T = 0, so why not use 0 as the lower limit and T as the upper limit?

AM
 
Alright, thank you very much, that makes sense
 

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