## Entropy change in constant pressure, and constant volume

$\Delta S = \frac{q_{rev}}{T}$

Jessica Yen Dis2G
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Joined: Fri Sep 25, 2015 3:00 am

### Entropy change in constant pressure, and constant volume

The question says: Assuming that the heat capacity of an ideal gas is independent of temperature, calculate the entropy change associated with raising the temerature of 1.00 mol of ideal gas atoms reversibly from 37.6 C to 157.9 C at (a) constant pressure and (b) constant volume.
I understand that we should use the equation: change in S=n*C*ln(T2/T1), but the solutions manual said that to find C at constant pressure of an ideal gas we put (5/2)*R, and to find C at constant volume we put (3/2)*R.
Why are these the heat capacities (C)? Will we have to know how to find the heat capacities of ideal gases under various circumstances (such as constant pressure, and constant volume)?

Chem_Mod
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### Re: Entropy change in constant pressure, and constant volume

The heat capacities of ideal gases come from the equipartition theorem and the theory of degrees of freedom, but you aren't responsible for them. It will suffice to memorize the values of 3/2 R and 5/2 R for a monatomic ideal gas.

005384106
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### Re: Entropy change in constant pressure, and constant volume

Why does R need to be multiplied by 3/2 for constant volume and 5/2 for constant pressure?

005384106
Posts: 101
Joined: Sat Aug 24, 2019 12:16 am

### Re: Entropy change in constant pressure, and constant volume

In what situation would you only use the R constant, 8.314 instead of multiplying the constant with a fraction?