# Thermodynamics Learning Goals Fa13

Learning goals for the first unit in our calculus-based physics 2 course…

**Content Learning Goals**

Upon completing this unit the student will be able to…

1. Differentiate between internal energy, heat, and work. The student will also be able to use the first law of thermodynamics to relate these quantities mathematically.

2. Construct a conceptual argument to justify the specific heat equation relating heat and temperature change. The student will also be able to use this equation to calculate temperature changes in various materials.

3. Explain the difference between an ideal gas and a real gas and explain under what conditions a real gas behaves approximately like an ideal gas.

4. Use the ideal gas law to relate (i.e. reason conceptually about or calculate numerical values for) pressure, volume, temperature and number of particles (or number of moles).

5. Explain the microscopic origin of gas pressure and explain conceptually why W = – ∫ P dV.

6. Use the ideal gas law together with W = – ∫ P dV to calculate work for various gas processes.

7. Explain the meaning of the equipartition theorem and use the theorem to calculate internal energy for an ideal gas of monatomic or diatomic molecules.

8. Explain the quantum mechanical limitations of the equipartition theorem.

9. Describe in words what it means for a process to be quasi-static, isothermal, or adiabatic and explain how these processes, as well as processes at constant pressure or constant volume, are achieved in the laboratory.

10. Represent the various processes described in (9) on a PV diagram and calculate Q, ΔU, and W for these processes.

11. Describe the processes that make up the Carnot Cycle and use the Carnot efficiency to relate Q_{out}, Q_{in}, T_{H}, T_{C}, and W.

12. Qualitatively explain what entropy measures and use the idea of microstates and macrostates to explain how the second law of thermodynamics is really a statement about probabilities.

13. Use the second law of thermodynamics and the expression to derive the maximum possible efficiency of a heat engine.

14. Explain why a refrigerator does not violate the second law of thermodynamics.

15. Use Excel or another computer program to numerically count microstates and explore entropy in systems of various sizes.

General Skills Related to this Unit

Every unit in this course will have learning goals specific to the topics of that unit. In addition, every unit will also emphasize some general skills that are applicable across much of science and beyond. The following general skills will be emphasized in this unit.

1. Thinking about large systems with many components in terms of averages, fluctuations around the average, and probabilities.

2. Thinking about a small system that can be worked out explicitly to gain insight to and identify trends in larger systems that are too large to work out explicitly.

3. Using equations involving several variables where one must be careful to keep track of what variables are fixed and what variables are allowed to vary in a given process.

4. Using integrals to add together many small contributions. This is how integrals enter into physical models. The usefulness of integrals in your life will depend upon your ability to see them as sums of very many tiny pieces.

5. Thinking about the idea of open vs. closed systems and how a system of interest can affect or be affected by its environment.

**Experiential Value of this Unit**

Each unit should also impact the way you view the world. I want you to see and experience things differently as a result of taking this class. The following are just some ways in which this unit might impact the way you view the world.

1. This unit will fundamentally change how you think about temperature. After finishing this unit you will literally be able to visualize temperature.

2. This unit will reveal the frenzy of activity that is constantly occurring at the microscopic scale. Scenarios you previously perceived as boring and static such as an inflated balloon lying on the ground will be revealed as dynamic and chaotic. This frenzy of activity will also deepen your appreciation for the role that collisions play in everything we see around us.

3. This unit will reveal that the world is truly governed by probabilities. You will discover that many of the phenomena we commonly think of as “impossible” are in reality merely improbable (*very* improbable). While you will never see the cream in your coffee spontaneously revert back into a droplet, there is a beauty and sense of awe in realizing that such an occurrence would not violate any laws of nature.

4. This unit will illustrate how nature can put fundamental limits on what can and cannot be achieved through engineering. This will deepen your respect for nature and the idea of fundamental limits while simultaneously adding to your appreciation for engineers and their achievements in the face of such fundamental limits.