A sample of an ideal gas in a

Question

A sample of an ideal gas in a cylinder of volume 3.11 L. at 298 K and 2.44 atm expands to 8.68 L by two different pathways Path A is an isothermal, reversible expansion. Path B has two steps. In the first step, the gas is cooled at constant volume to 1.10 atm. In the second step, the gas is heated and allowed to expand against a constant external pressure of 1.10 atm until the final volume is 8.68 L

Calculate the work for path A.

Calculate the work for path B.

J

Answer 1

PV = nRT

n = PV/RT = (2.44 atm)(3.11 L) / (0.0821 Latm/Kmol)(298K)

n = 0.310 moles

Path A:

For an isothermal expansion, we can use

w = -nRT ln(V2/V1)

w = work = ?

n = moles = 0.310

R = gas constant = 0.0821 Latm/Kmol

T = temperature in K = 298K

V2 = final volume = 8.68 L

V1 = initial volume = 3.11 L

w = -(0.310 mol)(0.0821 Latm/Kmol)(298K) ln (8.68/3.11)

w = -7.58 Latm x 1.03

w = -7.78 Latm x 101.325 J / Latm

w = -788 J

Path B:

w = -P∆V

w = work = ?

P = pressure = 1.10 atm

∆V = change in volume = 8.68 L - 3.11 L = 5.57 L

w = -(1.10 atm)(5.57 L) = -6.13 Latm x 101.325 J / Latm

w = -621 J