A rigid, thermally insulated vessel is divided by a thin partition. The left…

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Thermodynamic potentials and the formal structure of thermodynamics · Thermodynamic potentials and the formal structure of thermodynamics

Thermal Physics, Ch Chemical potential, open systems and chemical equilibrium

Problem

A rigid, thermally insulated vessel is divided by a thin partition. The left compartment holds

2.00\,\mathrm{mol}

of oxygen, the right holds

3.00\,\mathrm{mol}

of methane, and both are at

300\,\mathrm{K}

and

1.00\,\mathrm{bar} = 1.00\times10^{5}\,\mathrm{Pa}

. Both gases are ideal and no chemical reaction occurs. The partition is removed and the gases mix; since no heat enters and no work is done, the internal energy is unchanged and the temperature stays at

300\,\mathrm{K}

. ((a)) Using Chapter 6's entropy change for the isothermal expansion of an ideal gas, find by how much the entropy of the oxygen alone rises as it spreads through the whole vessel. ((b)) Hence find the total entropy change of the contents on mixing. ((c)) Find the change in the chemical potential of a methane molecule, from pure methane at

300\,\mathrm{K}

and

1.00\,\mathrm{bar}

to methane in the mixture at the same total pressure. ((d)) Find the change in the Gibbs energy of the whole contents from

\Delta G = \sum_i N_i\Delta\mu_i

, and check it against Chapter 7's

G = H - TS

with

\Delta H = 0

Browse the problem library