Question

12 moles of a gas is compressed isothermally and reversibly from 400 K , 1 bar to 1/2^th of its original volume. Initial volume of the gas was measured at 120 cm^3. Using the truncated virial EOS, calculate the required work for the compression.

Answer 1

Work done in isothermal reversible compression ,w,that satisfies the virial EOS is given by the equation,

w=nRT ln (V2/V1)

where n=12 mol

R=universal gas contant=8.314 J/K.mol

T=temperature=400 K

V2=120 cm^3=final volume

V1=1/12*120 cm^3=initial volume

The Virial EOS,

PVm =RT (1+B/Vm +C/Vm^2...) where Vm=V/n=molar volume]

P=RT/Vm (1+B/Vm +C/Vm^2...)=nRT/V (1+B/Vm +C/Vm^2...)

w=PdV=nRT(V2/V1 +B(Vm2^-1 -Vm1^-1)+....)

truncated EOS,w=nRT ln (V2/V1)=12mol*(8.314 J/K.mol)*400K ln(1/12)=-99165.667 J

work done=-99.165 KJ