Question

1. Show that for a classical ideal gas, Q1 alnQ1 NK Hint: Start with the partition function for the classical ideal gas ( Q1) and use above equation to find the value of right-hand side and compare with the value of r we derive in the class. (Recall entropy you derived for classical gas) NK Making use of the fact that the Helmholtz free energy A (N, V, T) of a thermodynamic system is an extensive property of the system. Show that 2. ДА N,T Hint: For an extensive property one can write, A (N, V, T) Nf (v, T) where v- V/N. Solve the left- hand side of the above equation for A (N, V, T) N f (v, T) 3. For a system of dipole with J- entropy (S) and the internal energy (U A + TS) has two orientations with energy ε pHcos. Derive the

Answer 1

1.

Notice that in equation 3, I have multiplied and divided by nK.

We have to show Nk ат" h N 2. N k Nos as we kne

2.

AN O N N eepin these n miAo vof(5) E N Cin Now we ase qve

AN Use (5) and (4)

3.

For 1/ alin e Par unchon RT t e Fee ereng

RT V3 RT