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

Wilson Yeh 1L
Posts: 42
Joined: Fri Sep 29, 2017 7:06 am

For the equation:
delta(S) from T1 to T2 = n*C*ln(T2/T1)

Where does the C come from? Is that supposed to be heat capacity, and of what exactly? Also, how would I go about solving a problem involving a change in temperature and entropy utilizing this equation if C isn't given? Thanks!

Ilan Shavolian 1K
Posts: 58
Joined: Fri Sep 29, 2017 7:03 am

I also don't get this. I know that for pressure it's Cp, and for volume it's Cv, but I don't exactly understand what that means.

Kelly Seto 2J
Posts: 30
Joined: Thu Jul 27, 2017 3:00 am

C is the just heat capacity of the system which we need to use in order to understand how much energy is needed to cause the temperature change in question. I don't think that there is a way to go about solving these without knowing the heat capacity for the system, however most of the questions want you to use Cv,m and Cp,m which are simply the molar heat capacities for different types of gases at constant volume or pressure, given by expressions found in the textbook such as 3/2*R, and then multiplying by the number of moles of the gas.

Angel Gomez 1K
Posts: 36
Joined: Fri Sep 29, 2017 7:04 am

By definition, an ideal gas is a gas made of point particles (zero dimensional/no volume particles). Therefore, treating any real gas as an ideal gas is always an approximation. While the approximation is closer for monatomic gases (He, Ne, etc.), we can apply it to any real gas.

The heat capacity to any monatomic ideal gas at:
1) constant volume is represented by $C_{V}$ and is equal to 3/2R, or
$C_{V}=3/2\cdot R$

2) constant pressure is represented by $C_{P}$ and is equal to 5/2R, or
$C_{P}=5/2\cdot R$

R is simply Rydberg's constant, or 8.314 J/K·mol.

If the volume doesn't change in your problem, you'll use 3/2R for heat capacity. If pressure doesn't change, you'll use 5/2R. This won't always be stated in the question and may be mentioned implicitly. Therefore, you just have to make sense of the problem at hand to determine which to use in some cases.