Question

9. (a) Show that for an infinitesimal reversible process in an ideal gas (? = Cp / Cv): dS = nR [dV/V + 1/(?-1) dT/T] (b) Now use your result from part (a) to show that the entropy difference S = S(T2, V2) - S(T1, V1) is given by ?S = nR [ln(V2/V1) + 1/(?-1) ln(T2/T1)] [HINT: Consider integration along the path C = C1 + C2 shown below]

          9. (a) Show that for an infinitesimal reversible process in an ideal gas (? = Cp / Cv):
dS = nR [dV/V + 1/(?-1) dT/T]
(b) Now use your result from part (a) to show that the entropy difference S = S(T2, V2) - S(T1, V1) is given by
?S = nR [ln(V2/V1) + 1/(?-1) ln(T2/T1)]
[HINT: Consider integration along the path C = C1 + C2 shown below]

9. (a) Show that for an infinitesimal reversible process in an ideal gas (? = Cp / Cv):
dS = nR [dV/V + 1/(?-1) dT/T]
(b) Now use your result from part (a) to show that the entropy difference S = S(T2, V2) - S(T1, V1) is given by
?S = nR [ln(V2/V1) + 1/(?-1) ln(T2/T1)]
[HINT: Consider integration along the path C = C1 + C2 shown below]

Added by Jonathan P.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sri K

07/30/2023

Step 1

Now, we are given that Y = Cp/Cv, where Cp is the molar heat capacity at constant pressure. We can rewrite this as: Cp = Y * Cv Since Cp - Cv = nR, we can substitute the expression for Cp in terms of Cv: Y * Cv - Cv = nR Now, we can factor out Cv: Cv * (Y - Show more…

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(a) Show that for an infinitesimal reversible process in an ideal gas (̳ = Cp / Cv): dS = nR [dV/V + 1/(̳-1) dT/T] (b) Now use your result from part (a) to show that the entropy difference S = S(T2, V2) - S(T1, V1) is given by ΔS = nR [ln(V2/V1) + 1/(̳-1) ln(T2/T1)] [HINT: Consider integration along the path C = C1 + C2 shown below]