Consider again the van der Waals EOS written in the form P = RT/V_m - b - a/V^2_
ID: 479402 • Letter: C
Question
Consider again the van der Waals EOS written in the form P = RT/V_m - b - a/V^2_m Calculate the quantity (partial differential U/partial differential V) Use your result from (a) to obtain an expression for the change in internal energy delta U_T = integral^V_m - f_V_m - i (partial differential U/partial differential V)_T dV_m Derive an expression for the work W required to compress the vdW gas isothermally from an initial volume of V_1 to a final volume V_2. Show that if a = b = 0, your expression in part (c) reduces to the result obtained in class for an ideal gas. Use your formula in part (c) to compute the work done on the surroundings by 1.80 mol of ethane when it expands from a volume of 0.002 m^3 to 0.004 m^3 at a constant temperature of 300K. (take the vdW constants for ethane to be a=0.554 J m^3/mol and b=6.38 times 10^- 5 m^3/mol) Repeat part (e) but assume an ideal gas. What is the % difference between the ideal gas and vdW results?Explanation / Answer
(a)
(dU/dV)T = T(dP/dT)v - P
dP/dT = R/V-b
dU/dV)T = T x R/(V-b ) - RT/V-b + a/V^2
= a/V^2
(b) now integrate part (a) .We get
a ( 1/Vf - 1/VI )
(c) work done = -pdV
= -RT ln( Vf -b / Vi - b) + a(1/Vf - 1/Vi )
(D) now on substituting a=b=0 ,
We. Get. -RT ln (Vf/Vi)
This is ideal gas equation.