Derive Z , U and C V in relation to G , T , P and/or derivatives of G with respect to T and P or ( ∂ G ∂ T ) P ( ∂ G ∂ P ) T Concept Introduction: The general correlation which define compressibility factor Z is Z = P V R T The fundamental property relation for internal energy U is defined as: G = H − T S G = U + P V − T S U = G − P V + T S And The fundamental property relation for heat capacity at constant volume C V is defined as: C V = ( ∂ U ∂ T ) V And the chain rule of partial derivatives or triple product rule is ( ∂ x ∂ y ) Z ( ∂ y ∂ z ) x ( ∂ z ∂ x ) y = − 1 And one useful equation derived from exact differentials in two dimensions, considering four state functions z , x , y and v and state space is two dimension and any of these four quantities are exact differential ( ∂ z ∂ y ) v = ( ∂ z ∂ y ) x + ( ∂ z ∂ x ) y ( ∂ x ∂ y ) v

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Chapter 6, Problem 6.91P

(a)

Interpretation Introduction

Interpretation:

Derive Z, U and CV in relation to G, T, P and/or derivatives of G with respect to T and P or (∂G∂T)P

(∂G∂P)T

Concept Introduction:

The general correlation which define compressibility factor Z is

Z=PVRT

The fundamental property relation for internal energy U is defined as:

G=H−TSG=U+PV−TSU=G−PV+TS

And

The fundamental property relation for heat capacity at constant volume CV is defined as:

CV=(∂U∂T)V

And the chain rule of partial derivatives or triple product rule is

(∂x∂y)Z(∂y∂z)x(∂z∂x)y=−1

And one useful equation derived from exact differentials in two dimensions, considering four state functions z,x,y and v and state space is two dimension and any of these four quantities are exact differential

(∂z∂y)v=(∂z∂y)x+(∂z∂x)y(∂x∂y)v

(b)

Interpretation Introduction

Interpretation:

Derive Z, H and CP in relation to A, T, V and/or derivatives of A with respect to T and V or (∂A∂T)V

(∂A∂V)T

Concept Introduction:

The general correlation which define compressibility factor Z is

Z=PVRT

The fundamental property relation for enthalpy H is defined as:

A=U−TSA=H−PV−TSH=A+PV+TS

And

The fundamental property relation for heat capacity at constant pressure CP is defined as:

CP=(∂H∂T)P

And the chain rule of partial derivatives or triple product rule is

(∂x∂y)Z(∂y∂z)x(∂z∂x)y=−1

And one useful equation derived from exact differentials in two dimensions, considering four state functions z,x,y and v and state space is two dimension and any of these four quantities are exact differential

(∂z∂y)v=(∂z∂y)x+(∂z∂x)y(∂x∂y)v

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