sandler_sm_06_18

# sandler_sm_06_18 - 6 6.18 Equation of state P(V b = RT(a FG...

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6.18 Equation of state PV b RT () = (a) P T R Vb P T V F H G I K J = = ; V T R P T P F H G I K J == ; and P V P T F H G I K J =− Thus CCT V T P T CT R P P T CR V V =+ F H G I K J F H G I K J =+ ⋅=+ for CP , we must have that T CT P , * = P C P T V T V T T V TT R P CTP CT T P P PP P P PP F H G I K J F H G I K J = F H G I K J = F H G I K J = 2 2 2 2 0 0, * Similarly, for CVT CT VV , * = , we must have that C V T P T T V V F H G I K J = F H G I K J = 2 2 0 . 2 2 0 P T T P R CTV CT V VV V F H G I K J = F H G I K J = =⇒ = , * af (b) First case is clearly a Joule-Thomson expansion = H constant T PC VT V TC RT P b RT P b C HP F H G I K J F H G I K J L N M O Q P + − L N M O Q P 11 PPP Since C is independent of P , integration can be done easily P CTd T bP P T T P z 1 2 21 a f to proceed, we need to know how depends on T . If is independent of T we have C p C p b C P (1)

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Eqn. (1) also holds if is a function of T , but then it is the average heat capacity over the temperature interval which appears in Eqn. (1). C P The second expansion is at constant entropy (key words are reversible and adiabatic)
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sandler_sm_06_18 - 6 6.18 Equation of state P(V b = RT(a FG...

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