Review from Last Lecture

1. Review from Last Lecture • Thermodynamic Processes • Isochoric (same volume) • Isobaric (same pressure) • Isothermal (same temp) • Adiabatic

2. Review from Last Lecture • 2nd Law of Thermodynamics • Heat can’t flow from cold to hot (w/o work) • Heat can’t be converted completely into work • Entropy can’t decrease (in isolated system) • Entropy • New state variable

3. Heat Engines • Imagine the following sequence • Heat gas at constant volume • Expand gas at constant pressure • Cool gas at constant volume • Compress gas at constant pressure • Work done is just the area inside the square! • Can also calculate the heat into the system and the efficiency

4. Carnot Engine • The Carnot cycle is another such cycle • Instead of isochoric and isobaric segments has adiabatic and isothermal segments • 1st Law dictates that work done is difference between heat flowing in and the heat flowing out • Adiabatic segments have no heat flow • Most efficient engine between these temps

5. Stirling Engine • The Stirling Cycle consists of isothermal and isochoric segments • Isothermal expansion (most of gas by hot resevior) • Move gas to cold resevoir • Isothermal compression (by cold resovoir) • Move gas to hot resovoir

6. The Equipartition Theorem • We defined the specific heat before as the heat required for a given temperature change • What’s really happening? • Imagine monatomic molecules (billiard balls) • As the temperature increases, the kinetic energy increases, but at what rate? • Imagine all the molecules restricted to a pipe • Then the average kinetic energy would increase as • Now imagine molecules restricted to a plane • Then the average kinetic energy would increase as

7. The Equipartition Theorem • We defined the specific heat before as the heat required for a given temperature change • For a monatomic ideal gas in 3D we have • This says that the increasing energy is shared equally between all the degrees of freedom (the three directions the molecule can move) • What about a diatomic gas?

8. The Equipartition Theorem • How many ways can a diatomic gas move? • Three translations • Two rotations (don’t count spinning along axis) • Vibration (counts as two because of kinetic and potential energy) • Thus we expect for a diatomic gas that

9. Freezing Out • What do we find for real gasses? • Most monatomic gasses have 5/2 R (at STP)! • At lower temperatures they behave just like monatomic gasses • Only at higher temps do they have CV=7/2 R.

10. Quantum Mechanics! • In fact, the diatomic molecules can only rotate at given rates: quantized rotation rates meaning quantized energies • If kT is much smaller than the jump from the lowest energy rotation (which is no rotation) to the next, then there is no room to share the energy