Question

Which of the following processes are spontaneous? For each process also indicate whether ΔS, ΔSsurr,and ΔSuniv, are positive, negative or zero:

a. The freezing of supercooled liquid water at −3°C and 1 bar.

b. The freezing of liquid water at 0°C and 1 bar by removing a small amount of heat.

c. The adiabatic expansion of a van der Waals gas into a vacuum.

d. The reversible isothermal compression of an ideal gas

Answer 1

a. ΔS of the system will be negative, as the liquid is supercooled there will be less freedom
of movement because it will solidfy because of the temperature drop.
ΔS_univ = ΔS_sys + ΔS_surr ;  ΔS_sys < 0 also  ΔS_surr > 0 (positive) since the heat will flow into
surroundings  ΔS_surr = -q_surr / T

b. ΔS_sys < 0 ; even after a small amount is removed ΔS_surr > 0
Since,  ΔS_univ = ΔS_sys + ΔS_surr ;   ΔS_univ > 0

c. For adiabatic expanison q_surr = 0 so ΔS_surr = 0 and the ΔS of the system will be positive
because when the gas expands there is more freedom for molecules to move i.e) more randomness.
Therefore ΔS_univ = ΔS_sys hence ΔS_univ > 0 (positive)

d. For reversible isothermal compression, ΔS of the system will be negative because the disorder
or randomness decreases. - ( ΔS_sys ) = ΔS_surr and ΔS_univ = 0 because it is reversible process.