Homework Help is Here – Start Your Trial Now!
Science
Advanced Physics
A Van der Waals gas has the following equation of state and internal energy aN²' P + Vz )(V – Nb) = NT aN² U = -Nt 2 V where t = kT, a and b are constants. All other variables have their regular meaning as defined in the textbook. (1) What variables in the above two equations are extensive variables, and what are non- extensive variables? Use scaling invariance to show that the two equations are consistent with the extensive and non-extensive variables.

A Van der Waals gas has the following equation of state and internal energy aN²' P + Vz )(V – Nb) = NT aN² U = -Nt 2 V where t = kT, a and b are constants. All other variables have their regular meaning as defined in the textbook. (1) What variables in the above two equations are extensive variables, and what are non- extensive variables? Use scaling invariance to show that the two equations are consistent with the extensive and non-extensive variables.

icon
Related questions
Question

ASAP!!

A Van der Waals gas has the following equation of state and internal energy aN2 V2 P + (V – Nb) = = Nt aN? U = NT 3 Nt - 2 V where t = kT, a and b are constants. All other variables have their regular meaning as defined in the textbook. (1) What variables in the above two equations are extensive variables, and what are non- extensive variables? Use scaling invariance to show that the two equations are consistent with the extensive and non-extensive variables. (2) Use the variables T, V and N, derive formulas for the following thermodynamic potentials through thermodynamic identities or Legendre transformation: S, H, F , G, and µ. Also derive Cy and Cp. Fix your integration constants with the formula for the entropy of ideal gas in the limit of N/V → 0, a → 0, and b → 0: Sideal = Nk{In nqr2- where no is quantum number state density which is a constant as a function of the Planck constant, ît, and molecular mass. Also Note the extensiveness of the variables.
Transcribed Image Text:A Van der Waals gas has the following equation of state and internal energy aN2 V2 P + (V – Nb) = = Nt aN? U = NT 3 Nt - 2 V where t = kT, a and b are constants. All other variables have their regular meaning as defined in the textbook. (1) What variables in the above two equations are extensive variables, and what are non- extensive variables? Use scaling invariance to show that the two equations are consistent with the extensive and non-extensive variables. (2) Use the variables T, V and N, derive formulas for the following thermodynamic potentials through thermodynamic identities or Legendre transformation: S, H, F , G, and µ. Also derive Cy and Cp. Fix your integration constants with the formula for the entropy of ideal gas in the limit of N/V → 0, a → 0, and b → 0: Sideal = Nk{In nqr2- where no is quantum number state density which is a constant as a function of the Planck constant, ît, and molecular mass. Also Note the extensiveness of the variables.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer