1. Calculate the entropy change for the system, the thermal surroundings, and the total entropy change for one mole of ice melting at +5^oC. The enthalpy change for melting ice is 6.03 kJ/mol.

2. Starting with the first and second law and efficiency defined as w/qhot, derive the Carnot efficiency equation for a heat engine.

3. Derive the equation:

DS = R ln(p₁ /p₂)

For the irreversible isothermal expansion of an ideal gas from p₁ to p₂.

4. Calculate q, w, DU, DH, and DS for the reversible isothermal expansion of 1 mole of N₂ from 2.5 bar to 0.75 bar.

5. Calculate q, w, DU, DH, and DS for the conversion of 2 mol of water to 2 mol of steam at 100 C and 1 bar. The heat of vaporization of water is 2260 J/g.

6. Derive the equation:

C_p ln(T₂/T₁) = R ln(p₂/p₁)

Starting with the SECOND LAW of thermodynamics.