### Exercise 1: Thermodynamics

```Exercise 1: Thermodynamics
General hint: Don’t forget to always be careful with the units.
1. Find the relationship that would be needed to compute the change in Helmholtz free energy
when the initial and final states are specified by the volume and pressure.
2. Compute the change in internal energy when 12 liter of argon gas at 273 K and 1 atm is
compressed to 6 l with the final pressure equal to 10 atm. Hint: Apply the general procedure
to evaluate U = U(P,V) for an ideal gas and integrate from initial to final (P,V)
3. Demonstrate that the change in a state function for a process is independent of the path by
calculating the change in enthalpy for two processes that change the state of 1 mol of a
monatomic ideal gas from (1 atm in a 20 liter container) to (1000 atm in a 100 liter container):
a. Process A: expand the gas at 1 atm from 20 to 100 liters, then increase the
pressure from 1 atm to 1000 atm to arrive at the final state.
b. Process B: compress the gas from 1 atm to 1000 atm in a 20 liter container,
then increase the volume to 100 liters.
4. The change in the Gibbs free energy upon forming 500 g of an equimolar (equal molar
fraction of each component) solution from SnCl4 and CCl4 at T = 500 K is Gmix = - 7.03 kJ.
The activity of SnCl4 in this solution is 0.52. What is the activity of the CCl4? Assume that the
standard states are pure components.
5. Does the entropy of a system increase or decrease when two ideal gases are mixed?
6. Reversible processes are a theoretical concept; they do not apply in the real world. Why,
then, is the concept so useful in thermodynamics?
7. What is the difference between a state function and a process variable? What is the
difference between extensive and intensive variables?
```