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We expect H to be proportional to

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We expect H to be proportional to

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  1. Setting:A rectangular slab of thickness Dx and with an area A.The front side of the slab is at a temperature T; the back side has a somewhat different temperature, T+DT.We are trying to calculate the heat-flow rate, the amount of heat flowing through the slab per unit time,H = DQ/Dt. We expect H to be proportional to the area of the slab, the temperature difference, DT, between the back and the front and inversely proportional to the thickness of the slab, Dx. H should also somehow depend of properties of the material the slab is made of…

  2. Bringing all the parts together: The coefficient k reflects specific properties of the material of the slab and is called thermal conductivity H = DQ/Dt – heat-flow rate is measured in Joules/second, J/s, or Watts, W.Thermal conductivity, k,is measured in W/mK.

  3. Thermal conductivities of different materials. Best heat conductor – Copper; use it when you build heat sink, as a material for pipes in your cooling system, a radiator. Worst heat conductors are the best insulating materials – air, fiberglass (layers in the walls of houses in cold regions), styrofoam (cups for your hot coffee).

  4. Heat-flow rate equation Is similar to the Ohm’s law: The current, I = Dq/Dt, amount of charge per unit time, is analogous to the heat-flow rate, H = DQ/Dt. The voltage, V, the factor driving the electric current, is analogous to temperature difference, DT. Continuing the analogy: electric resistance, R, is analogous to Thermal resistance is introduced as

  5. Thermal resistance is introduced as Heat-flow rate equation A composite slab is analogous to two resistors connected in a series. Heat-flow rate

  6. Reducing heat-flow rate for better thermal insulation. Better thermal insulation… red or blue?

  7. What about the door handles, when it is freezing outside? Which one would you prefer? Licking an ice cream, which is frozen, seems to be OK…

  8. In order to keep your tongue above 0 °C you basically have to heat the whole piece of metal… Otherwise… Cold metals are especially bad because of their high… thermal conductivity

  9. Thermal conductivities of different materials.

  10. A home heating system supplies heat at the maximum rate of 40 kW. If the house loses 1.1 kW for each °C between inside and outside, what is the minimal outdoor temperature for which the heating system can maintain 20 °C inside? Sample problem Solution:the lowest temperature outside for which the heating system can maintain 20 °C inside corresponds to the case, when the maximal power of the heater, Hmax=40 kW all flows outside because of temperature difference.

  11. 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.

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

  13. Fig. 11.8, p. 346 Slide 12

  14. Convection in the Earth mantle

  15. …and in the Sun

  16. Heat transfer by radiation. Stefan-Boltzmann law Total power, P [J/s=W], emitted by a hot object. ● 4th 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?

  17. 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. Gases The ideal gas law P is the pressure, V is the volume, T is the absolute temperature… Nis the total number of molecules in the gas and k is Boltzmann’s constant, k = 1.3810-23J/K

  18. 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.

  19. The ideal gas law Doubling the temperature, number of molecules, pressure? Keeping the volume and the number of particles constant, but doubling the temperature? Nis normally very big, while k is a very small number… NA= 6.0221023 – Avogadro number, number of molecules in 1 mole of a substance; n is the number of moles in the gas. R= 8.31 J/molK universal gas constant

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