![]() With solids, I would not expect pressure to significantly alter any entropy patterns they already have for small values for pressure that would otherwise be significant for gases.įor di/polyatomicsolids, we can consider either the complexity or the bond strength, as it relates to the number of "ways" it can exist. On the other hand, the change in volume of a liquid is appreciably low upon small increases in pressure that should substantially compress a gas, so the change in pressure of a liquid makes a smaller negative contribution to the change in entropy. (Regardless, the entropy of the universe is #>= 0#.) Therefore, if pressure increases, a negative contribution is made on the change in entropy of an ideal gas, but depending on the change in temperature, the actual change in entropy for the system might be positive or negative. Since #C_P# for a monatomic ideal gas is #C_V nR = 3/2nR nR = 5/2nR#, with #C_V# as the constant-volume heat capacity and the #3/2# coming from the three linear degrees of freedom ( #x,y,z#), this becomes: When we relate pressure then, to entropy, with #S = S(T,P)#:įor an ideal monatomic gas, #PV = nRT#, so: Which is what you would get for the Maxwell relation. Thus, utilizing this relationship and invoking the Product Rule on #d(PV)#, we get: #w_"rev" = -PdV#.Īnother relationship that relates with heat flow is the one for entropy and reversible heat flow: #q_"rev"# and #w_"rev"# are the most efficient (reversible) heat flow and work, respectively.#\mathbf(DeltaH = DeltaU Delta(PV)) = q_"rev" w_"rev" Delta(PV)# Starting from the first law of thermodynamics and the relationship of enthalpy #H# to internal energy #U#:
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