"Heat generally cannot spontaneously flow [i.e. the net vector] from a material at lower temperature to a material at higher temperature."or
“Heat doesn’t flow from cold to hot (without work input)”Note how this diagram from NASA of the second law of thermodynamics (without work input) illustrates the net flow of heat as a one-way vector always from hot to cold:
Work input is required to cause any heat to flow from cold to hot, which is obviously true from everyday experience. For example in a refrigerator, heat flows from cold to hot, but only when aided by an external agent (i.e. the compressor). Note that from the mathematical definition of entropy, a process in which heat flows from cold to hot has decreasing entropy. This can happen in a non-isolated system if entropy is created elsewhere, such that the total entropy is constant or increasing, as required by the second law. For example, the electrical energy going into a refrigerator is converted to heat and goes out the back, representing a net increase in entropy.
Another way of stating the Clausius formulation of relevance to the AGW debate is
"energy from the hotter body has left that body - it therefore cools down. The smaller amount of energy from the cooler body cannot fully replace that lost energy; it just slows the rate of cooling."Since "greenhouse" gases cannot add any energy to the system, or "work input", and are colder than the surface of the earth, they cannot cause additional warming of the earth; they just slow the rate of cooling. Furthermore, the "sunshade" or cooling effect of "greenhouse" gases outweighs the heating effect (due to absorption of incoming solar energy) by a factor of 100.
UPDATE: Alan Siddons (who is not the author of the above post) has just forwarded his reply to those questioning violation of the 2nd law of thermodynamics:
Key statement: The notion that colder matter does not radiate towards hotter matter defies common sense and causality.
I always see that weasel word: Toward. No doubt a cooler object does radiate "toward" a warmer object. The question is what happens as a result.
Say you have a blackbody plate (think of an electric heater) radiating 1000 W/m² toward another plate which, because of distance, absorbs half of that intensity, i.e., 500 W/m². At equilibrium, the receiving plate thus radiates 250 W/m² toward the 1000 W/m² plate. Question: Does the 1000 W/m² plate thereby rise to 1250 W/m²? If so, then, by raising the radiator’s temperature without adding more energy, you’ve disproved the first law of thermodynamics. Effectively, you’ve made the radiator heat itself. Moreover, now at 1250 W/m², the radiator will heat the other plate still more, absorb another dose of back-radiated energy, and will reach 1562 W/m². And so on, ad infinitum.
Either radiative heat transfer obeys the 2nd Law or it does not. If the 2nd Law does hold, then light can only transfer energy to something that is radiating less. This would mean that the physics of radiative forcing is fictitious.