- #1
owlman76
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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
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