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

Question

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.

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Arya 3 weeks 2021-10-01T10:18:04+00:00 1 Answer 0

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    2021-10-01T10:19:22+00:00

    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

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