Illustration 21.3: Entropy and Heat Exchange
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Animation 1 shows two objects of the same size, same mass, and same specific heat (mc = 2 for both), initially at different temperatures but in thermal contact with each other (temperature is given in kelvin and heat exchange is given in joules). The color-coded bars indicate the heat exchanged between the red and blue objects. Restart.
When two objects are in thermal contact with each other, we expect them to eventually reach the same temperature. However, there is nothing in the first law of thermodynamics that requires this. The only requirement from the first law is that energy be conserved, that the heat from one object goes into the other.
Try Animation 2. Is energy conserved? Does the heat from one go into the other? How does the heasxchange in this case compare with Animation 1? What you see in Animation 2, of course, does not happen, even though energy is conserved. The second law of thermodynamics, that entropy (in an isolated system) either increases or stays the same, governs this. The change in entropy, ΔS, is given by ΔS = ΔQ/T (for reversible processes at a constant temperature), and since Q = mcΔT, with a bit of calculus, you get
ΔS = mc ln (Tf/Ti),
where c is the specific heat capacity of a material and m is the mass of the material. What is the change in entropy for each object in the first animation? What is the total change in entropy? What about for the second animation? Notice that the net change in entropy for Animation 1 is positive, and in Animation 2 the net change in entropy is less than zero. According to the second law, processes don't naturally decrease entropy (it requires the input of energy), so what you see in Animation 2 does not occur in an isolated system because that would violate the second law of thermodynamics.
Illustration authored by Anne J. Cox.