Exam 1 / Midterm exam

See the first two sections in the ACS study guide for some practice problems. Available in the Good Library--on reserve.

Bring a calculator, pen/pencil, and a page of notes that you prepare ahead of time. You may refer to your notes during the exam, but no other resources or people. There will be a strict time limit of 1 hour for the exam. If you run out of time, you may finish unfinished problems after the exam, Your in-class score will be averaged with your post-exam score.

Topics covered

Chapter 1 of Carter

  • Kinds of systems.
  • Assumptions of equilibrium thermodynamics.
  • Covered all sections except 1.7. We only examined the first 1/3 or so of 1.7.

Appendix A and related notes/mathematics

  • The difference between exact and inexact differentials
  • A test for exact differentials
  • The Pfaffian: The differential of a quantity that depends on two independent variables.
  • The cyclic relations, which we occasionally use.
  • The method of separation of variables.

Chapter 2

  • Equation of state for an ideal gas
  • Equation of state for a Van der Waals gas
  • Phase separation (in a V.d.Waals gas): The difference between the ideal "single phase" V. d. Waals gas diagram below the critical temperature, with the two lobes, and the actual phase diagram, flat in temperature in the coexistence region.
  • What determines the critical temperature.
  • Influence and meaning of the $a$ and $b$ parameters for a V.d.W. gas
  • Interpreting phase diagrams and $P-v-T$ surfaces.
  • Interpreting the slope of the liquid-solid coexistence line, in terms of which phase is denser.
  • Sorting out extensive and intensive variables
  • Expansivity and compressability
  • Drawing diagrams of processes on $P-T$ / $P-v$ / $v-T$ diagrams.

Chapter 3

  • Work and Heat. Calculations for some simple processes.
  • The internal energy, $U$, of a system.
  • The first law: $dU=\delta Q-\delta W$, and the sign conventions for heat and work.
  • Review problem 3-8!

Chapter 4

  • Heat capacities, $C_v$ and $C_P$.
  • Latent heats (changes in enthalpy) for phase transitions.
  • Fig. 4.2: How knowing the latent heats for any 2 phase transitions near the Triple Point allows you to calculate the 3rd phase transition.
  • What's special about an ideal gas? $U$ and $H$ are functions of $T$ alone; Mayer's equation linking $C_v$ and $C_P$; The pressure-volume relation, $Pv^\gamma=K$ for an adiabatic process.
  • Calculations with heat capacities and latent heats, see problem 4.13.

Chapter 5

The midterm will only cover material up to and including Chapter 4.

  • The idea of a "heat engine" and the types and energies going in and out.
  • The Carnot cycle. Where heat / work energy enter or leave the system.
  • The efficiency of a Carnot heat engine and why that expression is important, compared to any other heat engine.
  • Calculations of efficiency (for a heat engine performing work) or coefficients of performance (for Carnot air conditioners or heat pumps) either from temperatures or heats and work.

Chapter 6

  • OK, there won't be anything about entropy. But you should be familiar with free expansion.