Question

2) Suppose that N2(g) may be described by the van der Waals equation of state. Ten moles of N, are isothermally and reversibly expanded from a volume of 1.01 to a volume of 10.02 at 300K. Compute the work done in the process. Is the result larger or smaller than the result obtained if the process involved an ideal gas? For N2(g): a = 1.352 atm dm mol-2; b = 3.87 x 10-2 dm² mol-

Answer 1

V-nb Vander-Waals ean for real gas" (P+n2a ) Cv- nb) 2 URT or p = MRI – B2a Now, workdone in isothermal expansion (reversible) for N2 will be : dwa – Par or W = - 1² MRI – n2a) or. nb Here, &,= 1 lit & a 10 dit and n=10 male. upon integrating all T = 300k get W = + MRT i V2-nb + an2 [ 1 ] 2 - - ] or-w = 10 x 0.083x 300 en 10-(10x 3.87x102) 1-(1043.87X10-2) + 1 352x(10)? [10-4 or w= 555.437 lit-atm! or Iw=-555. 437 dit atm. or lis 1 = 555.437 litatum V-nb at for ideal gars, work done in Isother mal reversible expansion till be: S -W- NRT in v or - W = 10x 0.082x300 en 10 or - W- 566. 436 dit atm . or (W = – 566 436 lit atin) or had 566. 436 lit-atm'

The tire sign implies work done by the system dwing expansion. so from the values obtained cul can conclude that the amount of work done by the system for the reversible expansion process will be larger for the édeal gas shan real gas.