Question

4 You have 1 mole of N2 gas in 50.0 dm3 at 200 K. Calculate q, w, OH, U, and OS associated with a reversible isothermal expansion to 100 dm3? You should assume N2 is a van der Waals gas (get the required information from your text)

Answer 1

q = 1152.56 J

w = -1152.56 J

delta H = 0

delta U = 0

delta S = 5.7628 JK-1

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For the reversible isothermal expansion of an ideal gas,

delta H = delta U = 0

q(rev) = -w(rev)

w(rev) = -nRTln(V2/V1)

delta S = q(rev) / T

Here,

n = no. of moles = 1

R = Gas constant = 8.314 J K-1 mol-1

T = Temperature = 200 K

V1 = volume before expanssion = 50 dm3

V2 = volume after expanssion = 100 dm3

w(rev) = -nRTln(V2/V1) = -1 x 8.314 x 200 x ln(100/50) = -1152.56 J

q(rev) = -w(rev) = 1152.56 J

delta S = q(rev) / T = 1152.56 / 200 = 5.7628 JK-1