### 9.7

Posted:

**Thu Feb 01, 2018 9:15 pm**Does anyone understand the equation Cp=5/2R? It is used in this problem and I don't understand what this equation is and why we need to use it for this problem.

Thanks!

Thanks!

Created by Dr. Laurence Lavelle

https://lavelle.chem.ucla.edu/forum/

https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=131&t=26707

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Posted: **Thu Feb 01, 2018 9:15 pm**

Does anyone understand the equation Cp=5/2R? It is used in this problem and I don't understand what this equation is and why we need to use it for this problem.

Thanks!

Thanks!

Posted: **Thu Feb 01, 2018 9:17 pm**

Cp means the heat capacity of a gas at constant pressure. We use this equation as part of the formula for calculating entropy in the problem, along with C_v, which is heat capacity for constant volume.

Posted: **Thu Feb 01, 2018 9:22 pm**

This refers to page 281 in the textbook. The Cp=5/2 R refers to molar heat capacity at a constant pressure for atoms. This comes from Cp = Cv + R, as Cv for atoms is 3/2R. We can use the molar heat capacity for atoms of ideal gas in this problem as it plugs into ΔS = n*Cp*ln(T2/T1). This formula derived by differentiation from dS = dq/T, where we plug in q=n*Cp*ΔT.

Posted: **Thu Feb 01, 2018 9:25 pm**

The change in molar internal energy of a monatomic ideal gas at a temperature T is (3/2)*deltaT. So, when calculating the molar heat capacity at constant volume, which is deltaU/deltaT, the quotient is (3/2)*T.

Since Cv is (3/2)*T, and Cp=Cv+R, Cp=(5/2)*T.

We substitute this equation in for C in the entropy calculation since the questions asks for the entropy of ideal gas atoms, which is monatomic.

Since Cv is (3/2)*T, and Cp=Cv+R, Cp=(5/2)*T.

We substitute this equation in for C in the entropy calculation since the questions asks for the entropy of ideal gas atoms, which is monatomic.