Why is Cv used in this example?

In summary, Cv and Cp are specific heat capacities that are used to calculate the change in entropy for a monatomic ideal gas. In this example, Cv is used because the process is not carried out at constant pressure or volume. Instead, the change in entropy is calculated using the ideal gas equation and the equation for ideal gas energy. The fact that c_V and c_P have the same value does not mean that the process occurs at constant volume or pressure.
  • #1
noob314
18
0
Can someone explain to me why Cv is used in this example?

Determine delta S for the conversion of a monatomic ideal gas from state 1 to state 2.
Cv = (3/2)R, Cp = (5/2)R
State 1: V1 = 22.0L, P1 = 1.25atm, T1 = 308K, n=0.917mol
State 2: V2 = 34.0L, P2 = 0.700atm, T2=325K, n=0.917mol


delta S = nR(V2/V1) + nCvln(T2/T1)

From what I can see, the process doesn't look like it's carried out in either constant pressure nor constant volume. If that answer is correct, then why is Cp not used?
 
Physics news on Phys.org
  • #2
The entropy change comes from the differential energy equation

[tex]dU=T\,dS-P\,dV\Rightarrow dS=\frac{dU}{T}+\frac{P\,dV}{T}[/tex]

the ideal gas equation

[tex]PV=nRT[/tex]

and the equation for ideal gas energy

[tex]U=U_0+nc_VT\Rightarrow dU=nc_V\,dT=n(c_P-R)dT[/tex]

[itex]c_V=c_P-R[/itex] is just a constant here. It doesn't imply that any process occurs at constant volume or pressure.
 

What is entropy change?

Entropy change is a measure of the disorder or randomness in a system. It is often described as the measure of the energy that is unavailable for work in a system.

How is entropy change calculated?

Entropy change can be calculated by taking the difference between the entropy of the final state and the initial state. This can be represented by the equation ΔS = Sfinal - Sinitial.

What factors affect entropy change?

The factors that affect entropy change include temperature, pressure, and molecular complexity. Generally, as temperature and pressure increase, so does entropy change.

Why does entropy increase in an isolated system?

In an isolated system, there is no exchange of energy or matter with the surroundings. This means that the molecules in the system have more freedom to move and arrange themselves randomly, leading to an increase in disorder and entropy.

How does entropy relate to the second law of thermodynamics?

The second law of thermodynamics states that the total entropy of a closed system will always increase over time. This is because energy transformations are never 100% efficient, leading to an increase in disorder and entropy in the system.

Similar threads

  • Introductory Physics Homework Help
Replies
8
Views
665
  • Biology and Chemistry Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
8
Views
761
  • Biology and Chemistry Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
10
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
678
  • Introductory Physics Homework Help
Replies
3
Views
900
  • Introductory Physics Homework Help
Replies
9
Views
5K
  • Thermodynamics
Replies
3
Views
1K
  • Biology and Chemistry Homework Help
Replies
2
Views
1K
Back
Top