Find equation of state of material usiing its compressability and expansivity.

[owlman76]

1. Homework Statement

A substance has an isothermal compressibility k= (aT^3)/(P^2) and an expansivity B = (bT^2)/P where a and b are constants, T is temperature, P is pressure. Find the equation of state of the substance.

2. Homework Equations

B= 1/v(dv/dT) (v is specific volume aka V/n)
K=-1/v(dv/dP) (v is specific volume aka V/n)

3. The Attempt at a Solution

If B= 1/v(dv/dT) then 1/v(dv/dT) = (bT^2)/P SOO (dv/dT) = (vbT^2)/P Using an indefinite integral I arrived at the answer (bvT^3)/3P + C for the equation of state.

If K = -1/v(dv/dP) then -1/v(dv/dP)= (aT^3)/(P^2) SOO (dv/dP) = (vaT^3) Using an indefinite integral I arrived at the answer (at^3v)/P + C

 

[member 553083]

for the equation of state.Therefore, the equation of state of the substance is (bt^3v)/3P + C + (at^3v)/P + C = (aT^3v + bT^3v)/3P +2C