derive maxwells thermodynamic general relations
Answers
Answer:This may help you
Explanation:
During the derivation of the equation we used the differential form of the first law of thermodynamics. We found that the rate of change of temperature with respect to volume at constant entropy, i.e., for adiabatic process, is equal to the rate of change of pressure with respect to entropy at constant volume.
Explanation:
THERMODYNAMIC POTENTIALS
A thermodynamic potential is some quantity used to represent some thermodynamic state in a system. We can define many thermodynamic potentials on a system and they each give a different measure of the "type" of energy the system has. In this article, we will consider four such potentials.
SIDE NOTE: NATURAL VARIABLES
Just a short note about natural variables before we begin. Consider a system undergoing some thermodynamic process which we are interested in analysing. Assume that we know that two quantities of that system will be constant throughout the process. Then, if we can find the thermodynamic potential whose natural variables are those quantities, then we can easily analyse the system using that potential. It's a natural choice to use that potential!
A natural variable of a thermodynamic potential is special because when the natural variables of a thermodynamic potential are held constant during a process, it means that we can easily use that potential to analyse the process because that thermodynamic potential will be conserved.
INTERNAL ENERGY
The first thermodynamic potential we will consider is internal energy, which will most likely be the one you're most familiar with from past studies of thermodynamics. The internal energy of a system is the energy contained in it. This is excluding any energy from outside of the system (due to any external forces) or the kinetic energy of a system as a whole. This is only the energy of the system due to the motion and interactions of the particles that make up the system.
Let's consider the first law of thermodynamics, which gives us a differetial form for the internal energy:
dU=δQ+δW
We know that the work done on a system,
δW, is given by: δW=−PdV
. Additionally, from the second law of thermodynamics, in terms of entropy, we know that the heat transferred is given by:
δQ=TdS.
Substituting this in the above expression for
dU, we get:
dU=TdS−PdV
This differential form is often known as the fundamental thermodynamic relation.
From the above we know that the natural variables of a thermodynamic potentials are the ones which, if kept constant, mean that the potential is conserved through some process. In this case this means that
dU=0
. This is achieved when
dS
and
d
lV
are both zero. So entropy, S, and volume, V, are the natural variables of internal energy, U