![]() ![]() In 1862 Clausius proposed that entropy is Δ S = ∫ d Q r e v T ĭuring each cycle of the heat engine, a net amount of heat, ΔQ enters the substance. Energy must be calculated, but the calculation can be verified by changing the system and monitoring how much heat energy and work is expended or released in order to achieve different values of volume and temperature.Ĭlausius definition of entropy ![]() It is generally understood that all state variables can be deduced from the volume and temperature: For example, one might place the piston in a heat bath of known temperature, fix the volume, and measure the pressure. These state variables include pressure (P), volume (V), energy (E), and temperature (T). This system can be usually be characterized by two state variables. In this essay we consider a simple thermodynamic system in which the number of particles is held fixed. Pressure, Volume, Energy, and Temperature (P,V,E,T) are state variables. State variables A sealed movable piston (without friction). A subdivision of a closed path into an arbitrarily large number of small Carnot cycles illustrates the concept. We then develop entropy for the ideal gas and use Carnot's theorem extend that result to all substances by arguing that all paths yield the same change in entropy. The argument that entropy exists as a state variable begins with the Carnot theorem, used to establish that all reversible heat engines have the same thermodynamic efficiency. The Clausius definition of entropy as, dS=k BdQ/T, fails to establish that entropy is a state variable until the integral of dS is shown to be path independent. Quasi-proof of the existence of entropy as a state variable 3 Proof that entropy is a state variable for all substances.1 Quasi-proof of the existence of entropy as a state variable. ![]()
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