Thermal Physics Unit T3 Thermodynamic Potentials

Prerequisites: T1 and T2

Overview: This unit introduces the "thermodynamic potentials" called the Helmholtz free energy F and the Gibbs free energy G which, together with the internal energy U and the enthalpy H form a group of four related thermodynamic quantities. Which of these will be used in a given situation depends mainly upon which set of two independent variables one wants to use.

F. W. Sears and G. L. Salinger, Thermodynamics, Kinetic Theory, and Statistical Thermodynamics (S&S) Chapt. 7 - Thermodynamic Potentials; Chapt. 8 - Applications of Thermodynamics to Simple Systems.

Comment: This unit involves some rather subtle ideas with great practical application. Make sure to get the definitions of the new quantities clear, and the appropriate pair of independent variables in each case.

After completing this unit you should understand:

1. U, the internal energy.
2. H, the enthalpy.
3. F, the Helmholtz free energy.
4. G, the Gibbs free energy.

Questions:

1. What is wrong with this argument? In the Joule-Thomson effect we are told that no heat enters or leaves the system. Thus dQ = 0 so dS = 0. We also derive H2 = H1, or dH = 0. But Eq. (37) says that dH = TdS +VdP, so we must have dP=0. But the pressure must change from one side of the plug to the other in order that the gas is push through and to have an effect. Therefore we can't have an effect!
2. Find the fallacy in the following argument: The first law says dU = dQ - PdV. If a system remains at constant volume no work will be done and PdV = 0, so dU = dQ. According to the definition of specific heat at constant volume dU = CV dT, so CV = (∂U/∂T)V. Then we can re-write the first law as dU =CV dT - PdV. In general dU = (∂U/∂V)T dV + (∂U/∂T)V dT, so (∂U/∂V)T = -P. However, in the special case of an ideal gas we know that the internal energy is independent of the volume so (∂U/∂V)T = 0, not -P. Explain this contradiction.

Problems:

Chapt. 7: Problem 6; Chapt. 8, Problems 1,6,10;

1. What is the Joule-Thomson coefficient for an ideal gas?
2. Obtain the expression for the Helmholtz free energy F for one mole of ideal gas. From this expression find the pressure P in terms of V and T.