The heat is used to expand the gas, and lift the piston. In the engine of a car the heat is generated by the combustion of an air-gas mixture. ![]() ![]() The one missing part is that we did not establish that entropy $S$ is a state function for an ideal gas, but this can be found in any introductory thermodynamics treatment (e.g. Entropy and the Second Law of Thermodynamics 19.1. All consequences of the Second Law can be derived from it, including the proposition that heat always spontaneously flows from hot to cold. In this chapter, we discuss the statements and consequences of the Second Law of Thermodynamics. This is a complete mathematical statement of the Second Law of Thermodynamics. The thermodynamics functions, entropy and free energy, those arise from the second law of thermodynamics play pivotal role in all branches of pure and applied science (physics, chemistry, biology and materials science). Which is the generalized Clausius inequality. We now define the state function entropy $S$ classically asįrom the previous inequality for reversible heat, we see that Combining this result with the First Law gives: Which means that the magnitude of work done by the system on the surroundings is maximal during a reversible process. ![]() Because $S_B-S_A$ is supposed to be macroscopic, such as $10^ The evolution $A\to B$ of macrostate $A$, containing $\exp(S_A)$ microstates, to macrostate $B$, containing $\exp(S_B)$ microstates, is easily shown by the formula for the probability "summing over final outcomes, averaging over initial states", to be $\exp(S_B-S_A)$ higher than the probability of the inverse process (with velocities reversed). It's simple to "roughly prove" the second law in the context of statistical physics.
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