Answer:
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
