Question

A certain systams ound to he Gibby G(P,T) = RT In (RT)5/2 where α and R are constants. Find the specific heat at constant pres- sure, Cp

Answer 1

we know that G= H-TS

dG= dH-TdS- SdT,      but VdP= dH-TdS

dG= VdP-SdT

at constant temperature,

dG= -SdT

(dG/dT)P= -S

S = -(dG/dT)P

G= RTln {(alpha*P)/ (RT)^5/2

G= RT *[ ln(alpha*P)- ln(RT)5/2]

G= RT* [ ln (alpha)*P - 5/2 * ln(RT)

differentiating the equation with respect to T at constant pressure

(dG/dT)_P= R* {( ln (alpha*P)} - 2.5* ln(RT)]- 2.5*RT/T = R*[ ln(alpha*P) - 2.5*ln(RT)- 2.5)

but (dG/dT)P= -S

hence -S= R [ ln(alpha*P)- 2.5 ln(RT)- 2.5]

S= R [ 2.5+2.5*ln(RT- ln(alpha*P)

(dS/dT)P= R (2.5)= 2.5R/T

but (dS/dT)P= CP/T, Cp =specific heat at constant pressure

hence CP/T= 2.5R/T

CP= 2.5R