Answer Key # 3 Thermodynamics - Edubirdie

University:
Santa Fe College
Course:
PHY 2048 | General Physics 1 with Calculus
Academic year:

2024
Views:

389

Pages:

4
Author:

Jabin F.

[ques. 36, page 36] P = αN^2T/V^2 => (∂P/∂T)v = αN^2/V^2 (∂U/∂V)τ = T(∂P/∂T)v - P = αN^2T/V^2 - αN^2T/V^2 = 0 U(T,V) dU = (∂U/∂T)v dT + (∂U/∂V)T dV ⇓ 0 dU = (∂U/∂T)v dT for isothermal process dT=0 dU=0 (option-a) [ques. 26, page 35] Cp - Cv = T(∂V/∂T)p(∂P/∂T)v α = 1/V(∂V/∂T)p Kτ = -1/V(∂V/∂P)τ cyclic chain: (∂P/∂T)v(∂T/∂V)p(∂V/∂P)τ= -1 (∂P/∂T)v =-1/((∂T/∂V)p (∂V/∂P)τ) = -(∂V/∂T)p/(∂V/∂P)τ Cp - Cv = T(∂V/∂T)p) (-(∂V/∂T)p)/(∂V/∂P)τ) Cp - Cv = -T((∂V/∂T)p)^2/(∂V/∂P)τ = -V^2T ((1/V (∂V/∂T)p)^2 / (V(1/V (∂V/∂P)τ) Cp - Cv = VT (1/V (∂V/∂T)p)^2 / (-1/V (∂V/∂P)τ) = VTα^2/Kτ [ques. 12, page 13] PV = nRT (∂V/∂T)p = R/P 1/V (∂V/∂T)p = R/VP = R/RT = 1/T (option - b) [ques. 8, page 28] b^3(P + a^2/V^3) = nRT (∂U/∂V)τ = a^2/V^3 U (T,V) dU = (∂U/∂T)v dT + (∂U/∂V)τ dV dU = CvdT + a^2/V^3 dV U = CvT - a^2/2V^2 + Uo U = const Ui = Uf CvTo - a^2/2(Vo/2)^2)) + Uo = CvTf - a^2/2Vo^2 + Uo Tf = To + 1/Cv(a^2/2Vo^2 - 2a^2/Vo^2) = To + a^2/CvVo^2 (1/2 - 2) Tf = To - 3a^2/2CvVo^2 (option-a)

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