Question

For a liquid obeying the equation ofstate Vm
= c1 + c2T+c3T2 -c4P− c5PT,findexpressionsfor each
of the following propertiesin terms ofthe c’s,CP,P, T, andV: (a)CP
-CV
;(b)(

Answer 1

The thermal expansivity coefficient $(\alpha)$ of a substance is the change in volume with temperature at constant pressure.

The equation for thermal expansivity is;

$\alpha(T,P)=$ $1\over V_m$ $($ $\partial V_m\over\partial T$ $)_p$

Where $(\alpha)=$ Thermal expansivity coefficient

$\partial V_m$ $=$ change in molar volume

$V_m=$ Molar volume

$\partial T=$ change in temperature

The isothermal compressibility coefficient$(k)$ of a substance is the change in volume with pressure at constant temperature.

The isothermal coefficient equation is;

$k(T,P)=$ $-1\over V_m$ $($ $\partial V_m\over \partial P$ $)_p$

The equation for$V_m$ is given by;

$V_m=C_1+C_2T+C_3T^2+C_4P-C_5PT$

Where $C_1,C_2,C_3,C_4,and C_5$ are constants.