![]() ![]() ![]() Accepting this as reasonable, we can now derive some very interesting, non-obvious truths. The second law isn’t violated so long as there is no way you could run the engine without the cold sink. That is, q1 -q2 = w, and energy is conserved. Sadie Carnot noted that a water wheel is able to extract work only when there is a flow of water from a high level to low similarly in a heat engine, you only get work by taking in heat energy from a hot heat-source and exhausting some of it to a colder heat-sink. That an engine can only extract work when there is a difference of temperatures is similar to the operation of a water wheel. This can be done with a thermopile, or with a steam engine (Rankine cycle, above), or a stirling engine. We find we can extract work from a system if we take heat from a hot body of water and deliver some of it to something at a lower temperature (the ice-cube say). We are now ready to put the first and second laws together. q + w = n ∆u where n is the grams of material, and ∆u is the change in internal energy per gram. We notice also that for any pure thing or mixture, the sum q +w for the change is proportional to the mass of the stuff we can thus say that internal energy is an intensive quality. The only way to leave things the same is if q + w = 0. This is a mathematical form of the first law of thermodynamics: you can’t take q + w out of nothing, or add it to something without making a change in the properties of the thing. Now, since for every path between two states, q +w is the same, we say that q + w represents a path-independent quantity for the system, one we call internal energy, U where ∆U = q + w. Still, each 4.174 joules counts as if it were 1 calorie. When adding heat or work, we say that q or w is positive when extracting heat or work, we say that q or w are negative quantities. If you input more heat, you have to add less work, and visa versa, but there is always the same sum. It’s the sum that’s constant, not the individual values so long as you count every 4.174 Joules of work as if it were 1 calorie of heat. ![]() In equation form, we say that, for any change, q +w is constant, where q is heat, and w is work. Similarly, if you want to cool something, a set amount of heat + work must be taken out. #Entropy of the universe plus#That is, if you want to heat some substance, that change requires that you put in a set amount of work plus heat. There is also a first law it states that energy is conserved. Thus, so long as time moves forward everything runs down in terms of work availability. To get useful work, you always need something some other transfer into or out of the system you always need to make something else hotter, colder, or provide some chemical or altitude changes that can not be reversed without adding more energy back. This observation is about as fundamental as any to understanding the world it is the basis of entropy and the second law of thermodynamics: you can never extract useful work from a uniform temperature body of water, say, just by making that water cooler. At best the entropy of the universe remains unchanged. You can not extract work from a heat source alone to extract work some heat must be deposited in a cold sink. ![]()
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