Thermodynamics

[master_lythos]

Hi,I got this question for a homework:

There is an uniform pole with length L, the temperature distribution on this pole has

the form

T = T1 +(l/L)(T2 − T1) (l is a small L)

initially, where T1 and T2 are the temperature at the end 1 and end 2 of the pole, l

is the distance between the point on the pole and end 1. Find the entropy change of

the pole after it arrives at thermodynamic equilibrium. Assume the heat capacity of

the pole at constant pressure is Cp.

My solution:

dS=(ds/dt)_pdT+(ds/dp)_TdP

(dS/dT)_p=C_p/T, a=(alpha) a_V=(1/V)*(dV/dT)_p

_{So then we have:}

dS=(C_p/T)dT because fo the constant pressure:

Thus: S=integral from T1 to T2 (C_p/T)dT = C_p*ln(T2/T1)

This is my answer, but it feel like im missing something, or should I derive the T i have from the begining and integrate on the path 0 to l?

btw, is it possible to write in latex here? If possible then how?

[imatfaal]

[latex]p_{\phi} \equiv \frac{\partial L}{\partial \dot{\phi}}[/latex]

 

We do have latex tags - just surround your code with thse tags (remove the underscore)

 

[_latex]p_{\phi} \equiv \frac{\partial L}{\partial \dot{\phi}}[_/latex]