Integrate the expression α=1/V (∂V/∂T)P assuming that α is independent of pressure. By doing so, obtain an expression for V as a function of T and α at constant P.

V(T)=Peᵅᵀ

Step-by-step explanation:

α= 1/V (dV/dT) P

Rearranging and separating variables

(α/P) dT = (1/V) dV

Taking the integrals of both sides

∫(α/P) dT = ∫(1/V) dV

αT/P = ln V + ln C, C a constant of integration

Taking the exponent of both sides

exp(αT/P) = exp(ln V + ln C)

exp(αT/P) = exp(ln V) X exp( ln C)

CV=exp(αT/P)

Since Pressure is constant, exp(P)= Constant, say K.

V(T)= Peᵅᵀ where Pressure= K/C