Thermodynamic potential Definition and 12 Threads

Suppose we have a gas of bosons with spin 0 and the grand potential is ##\Phi =\frac{kTV}{h^3} \int ln(1-e^{-\beta(p^2/2m -\mu})d^3p## we already integrated the function in the coordinate space and the result is the factor V (volume). Now, we know that ##\epsilon = p^2/2m## and ##d^3p = 4\pi...

Hello, I've been struggling with understanding how the molar fraction term appears in the expression of chemical potential as a fonction of pressure when the element is in a mixture, here is the proof given in my textbook for the expression of chemical potential of a pure substance (pure gas)...

I have a question about changing variables in the context of thermodynamics, but I suppose this would extend to any set of variables that have defined and nonzero partial derivatives on a given set of points. First I should define the variables. ##T## is temperature, ##U## is internal energy...

Why I cannot get the right answer by using △T=(3/2)nK△T to solve problem C：

Homework Statement a)Helium enters a closed system as a flow of compressed gas at a temperature of 14 K and at pressure p (enthalpy conserved). A fraction α emerges as liquid and the rest as gas at 14 K, both at atmospheric pressure p0. Find an expression for α in terms of the enthalpy H(p) of...

The Helmholtz function differential form for a reversible process is: dF = -SdT - PdV, as for a reversible process δW (by system/here an (ideal) gas) = PdV and dS = δQ/T. Therefore, for a reversible isothermal process, dT = 0 and hence dF = -PdV. Therefore, the work done by the system is W =...

Homework Statement Show that ##(\frac{\partial S}{\partial G})_Y = -\frac{C_Y}{TS}## Homework Equations ##G = H-TS, (\frac{\partial H}{\partial T})_Y = C_Y## The Attempt at a Solution ##dG = dH -TdS -SdT## and ##H## is a state variable so ## dH =\frac{\partial H}{\partial T} dT +...

I'm currently taking a Biophysics lecture. There's a vast usage of the terms Enthalpy and Gibbs Free Energy. I understood that most of the time, we're dealing with the Gibbs Free Energy, because our experiment is at constant Temperature (e.g. room temperature) and constant Pressure (e.g. 1 atm)...

Homework Statement One method for cooling a gas is adiabatic throttling (Joule-Thomson Experiment). Another method is a reversible adiabatic expansion. Show that if the initial and final pressures are the same, the difference in temperature obtained by the second method is always higher. Hint...

what is thermodynamic potential?

Homework Statement To state the differential form of the Helmholtz thermodynamic potential and derive the corresponding Maxwell's relation. Homework Equations Stated within the solution attempt. The Attempt at a Solution Helmholtz function: F = U - TS Calculating the...

i have studied my lecture notes back to front and looked high and low for a clue how to do this question but i tried in a) constructing an expression for u and came up with DU= +TDS -PDV - FDL BAUT I COULD BE MILES OUT. could anyone help. thanks here it goes: A piece of rubber of...