# Entropy Question

1. Sep 3, 2010

### p75213

This question appears in "Schaums Outline of College Physics". Please click the link:

http://www.4shared.com/photo/jbJ3lZwT/ScreenHunter_01_Sep_04_1256.html"

My question is how can they use this equation (delta S=(delta Q)/T) when the temperature is not constant? They treat it as being constant by taking the average temp.

Last edited by a moderator: Apr 25, 2017
2. Sep 3, 2010

### Andrew Mason

It is just an approximation to use the mean temperature over such a small temperature change. The point is to show that total entropy increases.

To do it accurately involves a bit of calculus:

$$\Delta S_h = \int_{340}^{338} dS = \int_{340}^{338} dQ/T = \int_{340}^{338} n_1C_v dt/T = n_1C_v\ln\left(\frac{338}{340}\right) \approx n_1C_v\left(\frac{2}{339}\right)$$

AM

Last edited by a moderator: Apr 25, 2017
3. Sep 4, 2010

### p75213

Thanks for the reply. I suspected that was the case.

4. Sep 4, 2010

### p75213

Elegant. I assume n1 is the mass.

Last edited: Sep 4, 2010
5. Sep 5, 2010

### Andrew Mason

I intended n1 to be the number of moles of the gas in the first compartment and C_v to have units of J/mole K. I probably should have used m and Cv in units of J/kg K, since that is what is used in this example.

AM