When Does Heat Transfer from a Colder Body to a Warmer One?
The answer is never. While radiant heat always transfers from a warmer to a cooler body, when cooler body is a good radiator, its emissivity is large and has little effect on radiant heat transfer for all temperature differences
Proof. Heat transfers between materials by three mechanisms: conduction, convection and radiation.
The rate laws are:
Conduction Q = Cp (Tw – Tc), Q is rate of heat transfer from w to c by conduction. Tw is temperature of warmer body, Tc is temperature of colder body, and Cp > 0 is heat capacity of material between w and c. By definition, Tw > Tc, so Q > 0.
Convection Q = Cv (Tw – Tc), Q is rate of heat transfer from w to c by convection. Tw is temperature of warmer body, Tc is temperature of colder body, and Cv > 0 is convection heat transfer coefficient of material between w and c. By definition, Tw > Tc, so Q > 0.
Radiation Q = σ Aw (Tw4 – Tc4) / [1/εw + Aw/Ac (1/εc – 1)]. Aw > 0 is radiating area of Tw, and Ac > 0 is radiating area of Tc. Denominator D = [1/εw + Aw/Ac (1/εc – 1)]. rate of radiant energy transfer between two dissimilar radiators – Google Search
If D < 0, then Q < 0 and heat flows from cooler Tc to warmer Tw. This cannot happen in nature because both εw and εc > 0, D > 0 and Q > 0.
However, as εc approaches 1, a good radiator, (1/εc – 1) approaches 0 and D approaches 1/εw. In that case Q approaches σ εw Aw (Tw4 – Tc4). This means the emissivity of c has little effect on Q.
In that situation raising atmospheric CO2 at 400 to 800 ppmv does not have much effect on Q and hence Earth’s surface radiating temperature, Tw.
If w is a poor radiator too, εw also approaches 0, and Q approaches 0 even when Tw > Tc. This means when both atmosphere and surface are poor radiators with low emissivity’s, Q is very small, no matter what the emissivity’s and Tw – Tc are.
This radiant heat transfer phenomenon was not properly included in global warming/climate change hoax analyses of 1995-2020.
Some parts of Earth atmosphere have low emissivity: N2 + O2 = 0, CO2 = 0.08. Surface is higher: water = 0.96, snow = 0.80-0.90, asphalt = 0.88. emissivity of co2 and h2o – Google Search emissivity of co2 and h2o – Google Search
Tom
| #
Like going to Neptune to get warmer.
Reply
Herb Rose
| #
Hi dr. Latour,
Bad science.
You’ve done the math but it has nothing to do with reality.
First you don’t understand what a thermometer is measuring. Energy is transferred to the thermometer by molecules colliding with it. It is not measuring kinetic energy but the amount of energy. The expanding material in it, like all matter, will have a limited range of what wavelengths it will absorb so it is not measuring radiated energy but kinetic energy. If you have a gas heater and increase the amount of fuel burning the temperature of the room will increase even though the flame burns at the same temperature. More kinetic energy is being transferred not a higher level of energy.
When an object radiates energy it does so in all directions and that energy decreases with distance from the source. A cooler object will only receive a small portion of the radiated energy and only be able to absorb certain wavelengths of the energy. The energy reaching the object will have a lower level than the energy being radiated so the level of energy can never equalize with the energy source. The moon will never get as hot as the surface of the sun. Objects do not equalize with other objects they equalize, radiating the same level amount of energy they are absorbing, bur equalize by gaining or losing energy to the energy field they are in.
Convection is an instantaneous equalization that occurs when molecules collide and follows the law of conservation of momentum. Energy flows from the object with the greater energy per unit mass to the object with less energy per unit mass, regardless of the masses. In elastic collisions there is no transfer of mass only energy. If you are in a small car and rear end a much larger truck going slower, your car will not speed up as energy flows from the truck, with more kinetic energy, to your car.
The O2 and N2 in the atmosphere absorb radiated energy and radiate energy just like all other matter. They absorb almost all the uv radiation before it reaches the surface and convert that energy into ke. The higher the altitude the greater the energy of the molecules. To compare the ke of molecules in the atmosphere divide the temperature by the density to get the ke energy for a constant number of molecules instead of the constant volume of molecules measured by the thermometer.
If what you claim were true the surface of the Earth could never cool at night because of the much hotter thermosphere surrounding it and we would be like Venus.
Herb
Reply