Question

19 g co2(g) is expanded isothermally at 40 c from 10 atm to 2 atm calculate w, q, h , u ,s

Answer 1

first find no. of moles of CO2(g) = given mass / molar mass = (19 g /44.0 g/mol) = 0.4318 moles

For an isothermal reversible expansion, the work is given by

w = -nRT ln (V2 / V1) ............1

The initial and final volumes are not given. However, for an isothermal process, from the ideal gas equation we have P1V1 = P2V2

V2 / V1 = P1 / P2 .........2

Substituting, the work can be calculated as

w = -nRT ln(P1/P2)

= -(0.4318 moles) (8.314 J/mol.K) (313 K) ln(10 atm /2 atm )

w = -1808.467 J

For gas, the differential of the internal energy is given by

dU = Cv dT...........3

and the differential of the enthalpy is given by

dH = CpdT ....4

Since the process is isothermal, dT = 0,

and so dU = 0 and dH = 0. Therefore

Finally, from the First Law of thermodynamics

dU = q + w .....5 since dU = 0

q = -w = 1808.467 J

dS = q /T = 5.77 J/K