2. The thermal equation of state of a simple liquid is given by ( V(T, P)=mathrm{V}_{0} exp left[mathrm{a}left(T-mathrm{T}_{0} ight)-mathrm{b}left(P-mathrm{P}_{0} ight) ight] ), where ( mathrm{V}_{0}, mathrm{~T}_{0}, mathrm{P}_{0} ), ( mathrm{a} ), and ( mathrm{b} ) are constants. a. Calculate (i) the thermal expansion coefficient ( (oldsymbol{alpha}) ) and (ii) the isothermal compressibility ( ( eta ) ). Show all the derivations. [ Hint: ( alpha=frac{1}{V}left(frac{partial V}{partial T} ight)_{P} equivleft(frac{partial ln V}{partial T} ight)_{P} ) [ left.eta=-frac{1}{V}left(frac{partial V}{partial P} ight)_{T} equiv-left(frac{partial ln V}{partial P} ight)_{T} ight] ] b. At a temperature, ( mathrm{T}=mathrm{T}_{0} ), calculate ( int_{mathrm{P}_{0}}^{2 mathrm{P}_{0}} V d P quad ) [Hint: ( int e^{a x} d x=frac{1}{a} e^{a x} ) ]
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**Part a (i): Calculate the thermal expansion coefficient (α)** Show more…
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