How do I solve for C in this entropy equation?

[jason177]

Homework Statement

Basically I'm given C_v = aT + bT³ when T<50K and where C_v 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 = C_v/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.

 

[Andrew Mason]

Homework Statement

Basically I'm given C_v = aT + bT³ when T<50K and where C_v 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 = C_v/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

 

[jason177]

Alright, thank you very much, that makes sense