(d) How does the expression c for the van der Waals gas compare Te PV -for an ideal gas? Explain the origin T to the equivalent expression of any difference, giving as much detail as possible.
(d) How does the expression c for the van der Waals gas compare Te PV -for an ideal gas? Explain the origin T to the equivalent expression of any difference, giving as much detail as possible.
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prioritize parts d and e please
Transcribed Image Text:3. Consider phase transitions in conditions of variable pressure, volume
and temperature. In the phase diagram for a single component system,
the critical point defines the pressure, Pc, and temperature, Tc, at the
end of the liquid-vapour co-existence line in P-T coordinates.
(a) Explain, with the aid of relevant diagrams in the appropriate
system of coordinates, and making reference to the concept of the
"critical isotherm", why at the critical point certain first and second
order partial derivatives are zero.
(b) A system consists of one mole of van der Waals gas, whose
equation of state is P+
a
V -b) = RT, where R is the universal
gas constant.
Using the information from (a) (ii), show that, for such a system, the
molar volume at the critical point is given by Ve = 3b.
(c) Show also that the other two parameters at the critical point are
8a
and
27 Rb
Te
Pe
276
(d) How does the expression c for the van der Waals gas compare
Te
PV
for an ideal gas? Explain the origin
T
to the equivalent expression
of any difference, giving as much detail as possible.
(e) Using the differential form of the Laws of Thermodynamics as a
starting point, and carefully listing all your assumptions, show the
sequence of steps that lead to the equation of the slope of the phase
dP
coexistence line, giving the slope
(the Clausius-Clapeyron
dT
equation).
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