![]() ![]() Overall, if you know the initial and final pressure, or the initial and final volume, you can figure out the change in entropy of a monatomic ideal gas at a constant temperature. Substitute this result back into (2) to get: #dA = stackrel("Numerator")overbrace(-S)" "stackrel("Hold constant")overbrace(dT) - P" "stackrel("Denominator")overbrace(dV)#ĭo something similar for #P, T, V# to get: The other way to express #DeltaS# involves equations (2) and (4): ![]() That means our first way to get the change in entropy is (plugging back into (1)): Then, for a monatomic ideal gas, we can use the ideal gas law ( #PV = nRT#) to give an explicit expression for the partial derivative of #V# with respect to #T# at a constant #P#: ![]() #dG = stackrel("Numerator")overbrace(-S)" "stackrel("Hold constant")overbrace(dT) + V" "stackrel("Denominator")overbrace(dP)# The first context in which we calculate #DeltaS# for an isothermal process involves looking at the cross-derivatives in (3) here is how you should examine #S,P,T#: It turns out that these can be derived from the Maxwell Relations that contain #T,P# or #T,V# as the variables that could potentially change:ĮNTROPY AS A FUNCTION OF TEMPERATURE AND PRESSURE It would be nice to have a way to get these relationships from known formulas, like the ideal gas law. If you notice, we don't have an expression for the way entropy changes due to pressure or volume in relation to gases. Q the heat transfer to or from the thermodynamic system. Using the change in entropy formula, we can compute the Entropy Change of a chemical reaction or a system: S (Q/T)rev. (1) #DeltaS = int_(P_1)^(P_2) ((delS)/(delP))_TdP# A thermodynamic system’s Entropy Change is denoted by S. When we hold temperature constant (an isothermal process), and change one of the other parameters: I assume that if you read further, you understand partial derivatives, cross-derivatives, and the integral of #1/x#.Įntropy is typically considered a function of temperature and either volume or pressure. Which means our two expressions are equivalent for any monatomic ideal gas.ĭISCLAIMER: This contains Calculus. Pick one, and you would use one of these:Īctually, if you notice that at constant #T# and #n# for a monatomic ideal gas, #P_1V_1 = P_2V_2#: It depends on which way we change the entropy (pressure or volume?). ![]()
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