1.) (1.5 point) Using the data table below for the following liquids, use the free-volume
theory we discussed in class to determine the AG'. Is there any relationship between
their molecular structure and interactions and AG'? For generality, you may assume that
8=1. You can also assume an average molecular weight of 200 g/mol, although this may
not be reasonable (why?); R134A is tetrafluoroethane.
2.) (1.5 point) The thermal conductivity of a liquid is more obscure than that of gases.
However, we can modify the kinetic theory approximation we derived for the thermal
conducted of a gas to apply to liquids. The average velocity of gas and liquid particles
can be written in terms of the absolute temperature and mass of the particles and the
speed of sound in the material (ca):
Vliquid = CAL*
In a liquid, the heat capacity at constant volume, Cv, is ~3R/Mw, instead of 3R/2Mw for
gases. The mean free path is the cube root of the volume per molecule of liquid:
A.) Determine an expression for k, the thermal conductivity (W/mK), in terms of
Avogadro's number, Boltzmann constant, heat capacities (Cv and CP), density, and speed
of sound (cu).
B.) Calculate the thermal conductivity for the following liquids (you can assume Cv/Cp~l).
C.) Compare these results with the experimental values
3.) (0.5 points) If we consider the kinetic theory expressions for the viscosity, thermal
conductivity, and diffusivity, we can express them in the following form:
u pCv k = 3Dag: JA,
The product of velocity and mean free path has the dimensions of length2/time, or
diffusivity. In the preceding equation, all quantities on the left-hand side represent a
diffusivity, specifically the same diffusivity. Comment on what this means for the
mechanism whereby mass, energy, and momentum are transported in gas. Would you
expect the same type of mechanism to operate in a liquid? In a solid? What would be
required for the same mechanism to operate?
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