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Discussion :: Chemical Engineering Thermodynamics

  1. The expression for entropy change given by, ΔS = nR ln (V₂/V₁) + nCv ln (T₂/T₁) is valid for

    2. A.

     Reversible isothermal volume change
    B.

     Heating of a substance
    C.

     Cooling of a substance
    D.

     Simultaneous heating and expansion of an ideal gas

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    Answer : Option D

    Explanation :

    For a pure substance in a closed system has a degree of freedom = 2
    So, entropy(s) can be expressed as a function of two variables (properties) S=fn(T,V)

    ⇒dS=(∂S∂T)VdT+(∂S∂v)TdT⇒dS=CVdTT+(∂P∂T)VdV(for one mole of ideal gas(∂P∂T)V=RV)⇒dS=CVTdT+nRVdV
    So, on integrating this equation from temperature T2 to T1 expanding volume from V1 to V2 GIVES the equation

    ΔS=nRln(V2V1)+nCvln(T2T1)

    for an ideal gas of n moles.

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