1. Convection - Heat transfer in a gas or liquid by the circulation of currents from one region to another. Can be forced or spontaneous (natural). Hot and cold liquid is brought in a thermal contact; it reduces the distance across which the conduction occurs and increases the contact area.

2. Reducing heat-flow rate for better thermal insulation. Thick (large  x ) cavities in house walls filled with insulating (small k ) materials; Reducing the number of walls (small surface area A ).

4. Heat transfer by radiation. Stefan-Boltzmann law Total power, P [J/s=W], emitted by a hot object. ● 4 th power of the absolute temperature, T. ● Surface area, A. ● Emissivity of the material, e. ● Stefan-Boltzmann constant, Emissivity, e, varies between 1 (black body) and 0 (reflecting surface). A good emitter of radiation ( e ≈ 1) is also a good absorber. A radiator and a solar heater should be black. A thermos bottle should be silver-coated. Emissivity, e, depends on the wavelength of the radiation. For a solar heater, what values of e are the best for sunlight and for thermal waves radiated near 100 °C?

5. Gases Gas is matter in a rarefied state. The molecules are moving freely most of the time, and only once in a while undergo short-term collisions. The macroscopic state of a gas in thermodynamic equilibrium is determined completely by its temperature, pressure, and volume. The ideal gas law P is the pressure, V is the volume, T is the absolute temperature… N is the total number of molecules in the gas and k is Boltzmann’s constant, k = 1.38  10 -23 J/K

6. The ideal gas law Gas in a cylinder under a piston Pressure, P, is given by Where m is the total mass of the piston and the lead and A is the area of the piston. We can: add or remove the lead shots to change the pressure of the gas; tune the temperature of the thermal reservoir.

7. The ideal gas law Doubling the temperature, number of molecules, pressure? Keeping the volume and the number of particles constant, but doubling the temperature? N is normally very big, while k is a very small number… N A = 6.022  10 23 – Avogadro number, number of molecules in 1 mol of a substance; n is the number of moles in the gas. R = 8.31 J/mol  K universal gas constant

8. Kinetic theory of the ideal gas Kinetic energy is the only form of molecular energy that is important and it is preserved in the collision events.

9. L Collisions of the gas molecules with a wall.. As a result of a collision the momentum changes by Force due to one molecule as a function of time

10. Collisions of the gas molecules with a wall (cont.) Newton’s second law for an instantaneous force: Now  t is a long time interval – the time between two consecutive collisions with the wall. For the average force on the wall it becomes: change of momentum in a collision time between collisions

11. Now  t is – the time between two consecutive collisions with the wall. L

12. Kinetic theory of the ideal gas. Let’s try to account for all molecules of the gas:

13. L Kinetic theory of the ideal gas. Pressure on the wall with surface area A : Velocity of a molecule: The average velocity – average of a sum is equal to the sum of averages… All the directions of motion (x, y, z) are equally probable! V – volume of the box.

14. L Pressure on the wall with surface area A : The average kinetic energy of a molecule The ideal gas law (experimental fact!) Therefore: