1. Consider the isothermal compression of 0.250 mole of gas by a movable piston

Question

1. 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 °C. a. Treating the gas ideally, show that the work done is w = +3293 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) b. Treating the gas using the van der Waals formula with a = 4.48 atm ×L2xmol-2 and b = 0.332 Lxmofi show that the work done is w= +3341 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

form the given data

n = 0.25

Vi = 5.2 L

Vf = 3.65 L

T = 100C = 373.16 K

b. from wan der walls formula

(P + an^2/V^2)(V/n - b) = RT

final pressure = Pf

a = 4.48 atm L^2 mol ^-2

b = 0.332 L / mol

(Pf + 4.48*0.25^2/3.65^2)(3.65/0.25 - 0.332) = 0.082057*373.16

Pf = 2.125071 atm

hecne irr work W = Pf(Vf - Vi) = 3.29386 atm lit = 332.67992 J

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