Answer:
Explanation:
Given
Temperature of solid 
Einstein Temperature 
Heat Capacity in the Einstein model is given by
![C_v=3R\left [ \frac{T_E}{T}\right ]^2\frac{e^{\frac{T_E}{T}}}{\left ( e^{\frac{T_E}{T}}-1\right )^2}](https://tex.z-dn.net/?f=C_v%3D3R%5Cleft%20%5B%20%5Cfrac%7BT_E%7D%7BT%7D%5Cright%20%5D%5E2%5Cfrac%7Be%5E%7B%5Cfrac%7BT_E%7D%7BT%7D%7D%7D%7B%5Cleft%20%28%20e%5E%7B%5Cfrac%7BT_E%7D%7BT%7D%7D-1%5Cright%20%29%5E2%7D)

Substitute the values


Answer:
a)W=12.62 kJ/mol
b)W=12.59 kJ/mol
Explanation:
At T = 100 °C the second and third virial coefficients are
B = -242.5 cm^3 mol^-1
C = 25200 cm^6 mo1^-2
Now according isothermal work of one mole methyl gas is
W=-
a=
b=
from virial equation

And

a=
b=
Now calculate V1 and V2 at given condition

Substitute given values
= 1 x 10^5 , T = 373.15 and given values of coefficients we get

Solve for V1 by iterative or alternative cubic equation solver we get

Similarly solve for state 2 at P2 = 50 bar we get

Now

a=241.33
b=30780
After performing integration we get work done on the system is
W=12.62 kJ/mol
(b) for Z = 1 + B' P +C' P^2 = PV/RT by performing differential we get
dV=RT(-1/p^2+0+C')dP
Hence work done on the system is

a=
b=
by substituting given limit and P = 1 bar , P2 = 50 bar and T = 373 K we get work
W=12.59 kJ/mol
The work by differ between a and b because the conversion of constant of virial coefficients are valid only for infinite series
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