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

Answer 1

∫ β δT = ∫ 1/V δV

Since β independant of T, ∫ β δT = βT + constant.
βT = ∫ 1/V δV

Use ∫ 1/x dx = ln(x) + constant
βT = ln(V) + constant

.: V = k e^(βT)

Answer 2

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