Consider a sample of 2.75 moles of argon contained in a 1.50 L piston at 298 K.

Question

Consider a sample of 2.75 moles of argon contained in a 1.50 L piston at 298 K. a. The gas is heated isothermally at a constant pressure, causing it to expand to a final volume of 5.05 L. Given that the molar heat capacity of argon at constant pressure (C_pn) is 20.786 J K^-1 mol^-1, calculate q, w, Delta H, and Delta U b. Calculate q, w, Delta H, and Delta U if the gas instead expands reversibly and isothermally to a final volume of 5.05 L c. Calculate q, w Delta H, and Delta U if the gas instead expands reversibly and adiabatically to a final volume of 5.05 L.

Explanation / Answer

a. work done (w) = nRTln(V2/V1)

                           = 2.75 x 8.314 x 298 ln(5.05/1.5) = 8270.85 J

q = w = 8270.85 J

dU = 0

dH = 0

b. work done (w) = -nRTln(V2/V1)

                           = -2.75 x 8.314 x 298 ln(5.05/1.5) = -8270.85 J

q = -w = -8270.85 J

dU = 0

dH = 0

c. work done (w) = nPdV

                           = 2.75 x (2.75 x 0.08205 x 298/1.5) (5.05 - 1.5) x 101.33 = 44.344 kJ

q = 0

dU = w = 44.344 kJ

Cp = Cv + R = 20.786 + 8.314 = 29.1 J/K

T2 = 1.5 x 298/5.05 = 88.515 K

dH = CpdT = 29.1 (88.515 - 298) = -6096.01 J

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