In lecture we showed the relationship between chemical potential vs$.$ T & P$.$

$(\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{T}}{)}_P=\frac{-}{b}ar(S),(\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{P}}{)}_T\frac{?}{b}=ar(V)$

a$.$ For temperature, is $(\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{T}}{)}_P$ always positive, always negative, or does it vary? Explain

briefly.

b$.$ Predict the relative magnitudes of $(\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{T}}{)}_P$ for a solid, liquid, or gas. Can this be

rationalized by thinking about trends in molar entropy for these three phases?

Explain briefly.

c$.$ Sketch a graph of $$ vs$.$ T for solid, liquid, and gas at constant pressure. Your graph

should be consistent with your answers to a and $b.$

d$.$ For pressure, is $(\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{P}}{)}_T$ always positive, always negative, or does it vary? Explain

briefly.

e$.$ Predict the relative magnitudes for $(\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{P}}{)}_T$ for a solid, liquid, or gas. Can this be

rationalized by thinking about trends in molar volume for these three phases?

Explain briefly.

f$.$ Sketch a graph of $$ vs$.$ P for solid, liquid, and gas at constant temperature. Your

graph should be consistent with your answers to $d$ and $e.$

Please Make sure everything is correct because I$\text{'}$m having wrong answers on chegg always and that is affecting my academic goals badly. Thank you so much for your help