Question

One mole of carbon dioxide gas occupies a volume of 24.346 L at 25 ºC. It is slowly compressed isothermally to a volume of 12.173 L. Assume that CO2 behaves as a van der Waals gas. It is known that, for a van der Waals gas, , dU = a n2 V-2 dV. Find

a. w, the work done in Joules on the gas during the compression (10 pts)

b. q, the heat flow in Joules into the gas during the compression

Answer 1

for isothermal compression of Vanderwaal gas , work done= -PdV

but for vanderwaal gas for one mole, (P+a/V²)*(V-b)= RT, P= RT/(V-b)- a/V²

work done = RTln {(V1-b)/(V2-b)} +a*(1/V₂-1/V₁)

for Vanderwall gas a= 3.610L²atm/mole² and b= 0.0429 L/mole

1st term of work of equation = 8.314 J/mole.K*298ln{(24.346-0.0429)/(12.173-0.0429)}=1722 joules

second term = 3.610*(1/12.173-1/24.346) L.atm=0.148 L.atm but L.atm= 101.3 J

hence second term = 0.148*101.3= 15 joules

total work done = 1722+15= 1737 joules

change in internal energy = (an2/V2)*dV

n= 1, the change in internal energy= (a/V²)*dV

when integrated, change in internal energy= a*(1/V1-1/V2)

this also need to be converted to joules by multiplying with 101.3

hecne change in internal energy= 3.610*(1/12.173-1/24.346)*101.3 joules =15 joules

deltaU= Q+W

Q= deltaU-W=-1537 joules