Section A: short answer

You must correctly answer 3 of 4 questions to receive an assignment grade higher than 3.

Question 1

Describe what is meant by two systems being in thermodynamic equilibrium.

Question 2

What is the equipartition theorem and the condition of its validity?

Question 3

Calculate the internal energy of one mole ideal gas at room temperature for both a monatomic gas and a diatomic gas.

Question 4

Write an explicit integral for the work done upon isothermal expansion of a van der Waals gas from an initial volume Vi to a final volume Vf . Use the equation of state for a van der Waals gas . Note: you do not need to do the actual integration.

Section B: long answer

Your assignment grade will equal your average mark from Section B if you meet the threshold in Section A. Otherwise, it will equal the minimum of this average and 3. Note: you should assess all answers.

Question 1

(7 marks)

Consider a container that is initially at atmospheric pressure with volume 咲=5 litre and holds five kilograms of carbon dioxide. The container is compressed to a final volume Vf = 0.2 litres. During the compression, its pressure changes with volume as

p (v )=Pi(j)², ⑴

where Pi is the initial pressure.

(a) Sketch a graph of pressure versus volume for this process.

(b) Calculate the work done on the gas during this process, assuming that there are no other types of work being done.

(c) Calculate the change in the energy content of the gas during this process.

(d) Calculate the amount of heat added to or removed from the gas during this process.

(e) Describe how you might arrange an experiment where the pressure and the volume satisfy Eq.(1).

Question 2

(7 marks)

A cylinder filled with nitrogen gas expands from 10 to 100 litres. It is initially at atmospheric pressure and room temperature (Ti = 298 K).

(a) Determine the work done by the gas and its final temperature, assuming the expansion process is isothermal.

(b) Perform the same calculations for an adiabatic expansion.

(c) Explain the differences between the results of (a) and (b).

Thermodynamic Properties of Selected Substances

All of the values in this table are for one mole of material at 298 K and 1 bar. Following the chemical formula is the form of the substance, either solid (s), liquid (1), gas (g), or aqueous solution (aq). When there is more than one common solid form, the mineral name or crystal structure is indicated. Data for aqueous solutions are at a standard concentration of 1 mole per kilogram water. The enthalpy and Gibbs free energy of formation, *H and AyG, represent the changes in H and G upon forming one mole of the material starting with elements in their most stable pure states (e.g., C (graphite), O2 (g), etc.). To obtain the value of AH or AG for another reaction, subtract Ay of the reactants from Ay of the products* For ions in solution there is an ambiguity in dividing thermodynamic quantities between the positive and negative ions; by convention, H⁺ is assigned the value zero and all others are chosen to be consistent with this value. Data from Atkins (1998), Lide (1994), and Anderson (1996). Please note that, while these data are sufficiently accurate and consistent for the examples and problems in this textbook, not all of the digits shown are necessarily significant; for research purposes you should always consult original literature to determine experimental uncertainties.