Consider the isothermal compression of 0.250 mole of gas by a movable piston whi
ID: 711045 • Letter: C
Question
Consider the isothermal compression of 0.250 mole of gas by a movable piston which takes the system from an initial volume of 5.20 L to a final volume of 3.65 L at a temperature of 100 oC.
Treating the gas using the van der Waals formula with a = 4.48 atm ×L2×mol-2 and b = 0.332 L×mol-1, show that the work done is w = +334 J if the process is carried out irreversibly. (Hint: in order for the movable piston to pull this off it must push on the gas with a constant pressure so that the pushing ceases when the gas reaches the final volume)
Explanation / Answer
given,
n=0.25moles
v1=5.20 L
v2=3.65 L
a=4.48 atm mol-2 L2
b=0.332 L mol-1
T=100o c=273+100=373 k
we have to find pressure at final volume which remains constant throughout th process as it is irreversible process.
vander waals equation=(p +(an2)/v2)(v-nb)=nRT.
substituting the corresponding values
(p +(4.48*(0.25)2)/3.652)(3.65-0.25*0.332)=0.25(0.082057)(373)
(p + 0.02)(14.268)=30.586
above equation gives the pressure in atm .
p=2.1236atm
work done in irreverisble process= -p(v2-v1)
= -2.1236(3.65-5.20)
=3.29158Latm
1Latm=101.33 j
workdone=3.29158*101.33= 333.53 J
hence proved