Entropy And Energy Representation

AI Thread Summary
The discussion focuses on converting the entropy of a system, represented as S(U,V,N), into its internal energy U(S,V,N). An example provided is for an ideal classical gas, where the entropy equation includes terms involving the Boltzmann constant, particle number, and volume. The conversion to internal energy is achieved through algebraic manipulation, specifically isolating ln(U/N) and applying the exponential function. The final expression for internal energy is U=N*(U/N)^(2/3)*exp[(2/3)*(S/(N*R)-c)]. The discussion emphasizes that this process is primarily algebraic in nature.
hurz
Messages
7
Reaction score
0
How do I go from the entropy of a system, S(U,V,N), to its internal energy, U(S,V,N)?
For instance, for an ideal classical gas, we have

S=(3/2)N*R*ln(U/N) + N*R(V/N) + N*R*c

where R is the Boltzmann constant, N is the particle number, V is the volume and "c" is a constant.

How can I convert this to U(S,V,N) ?

The unswer is U=N*(U/N)^(2/3)*exp[(2/3)*(S/(N*R)-c)]

Regards,
hurz.
 
Science news on Phys.org
This is just algebra. Isolate ln(U/N), use e^() on both sides and multiply with N.
 
my bad. thanks!
 

Thread 'Condensate rate of water for an air conditioning cooling coil'

I need to calculate the amount of water condensed from a DX cooling coil per hour given the size of the expansion coil (the total condensing surface area), the incoming air temperature, the amount of air flow from the fan, the BTU capacity of the compressor and the incoming air humidity. There are lots of condenser calculators around but they all need the air flow and incoming and outgoing humidity and then give a total volume of condensed water but I need more than that. The size of the...
View full post »

Thread 'Entropy and configurations of microstates'

I was watching a Khan Academy video on entropy called: Reconciling thermodynamic and state definitions of entropy. So in the video it says: Let's say I have a container. And in that container, I have gas particles and they're bouncing around like gas particles tend to do, creating some pressure on the container of a certain volume. And let's say I have n particles. Now, each of these particles could be in x different states. Now, if each of them can be in x different states, how many total...
View full post »
Thread 'Why work is PdV and not (P+dP)dV in an isothermal process?'

Thread 'Why work is PdV and not (P+dP)dV in an isothermal process?'

Let's say we have a cylinder of volume V1 with a frictionless movable piston and some gas trapped inside with pressure P1 and temperature T1. On top of the piston lay some small pebbles that add weight and essentially create the pressure P1. Also the system is inside a reservoir of water that keeps its temperature constant at T1. The system is in equilibrium at V1, P1, T1. Now let's say i put another very small pebble on top of the piston (0,00001kg) and after some seconds the system...
View full post »

Similar threads

I Does Callen's Entropy Expression for a General Ideal Gas Contain an Error?
Replies
19
Views
2K
I Helmholtz entropy of ideal gas mixture is additive?
Replies
3
Views
2K
I How can the maximum entropy and minimum energy principles be physical?
Replies
13
Views
3K
Thermodynamic equation of differentials (and how to work with them)
Replies
1
Views
1K
A Equilibrium, entropy, probability - Release of constraints
Replies
2
Views
1K
Why does the entropy of a closed system remain constant in a reversible process?
Replies
10
Views
3K
I Understand the Thermodynamic Identity: Is This Correct?
Replies
3
Views
2K
I Why Should the Total Number of States Equal the Volume of an Octant?
Replies
7
Views
2K
I The Equilibrium Macrostate: Reif's Statistical Physics
Replies
15
Views
1K
Euler's equation of thermodynamics in free expansion (Joule expansion)
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top