Schaums Outline: Entropy Ques - Tmp Not Constant

[p75213]

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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.

 

[Andrew Mason]

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

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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.

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

 

[p75213]

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

 

[p75213]

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

Elegant. I assume n1 is the mass.

 

[Andrew Mason]

Elegant. I assume n1 is the mass.

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