When a molecule of a liquid approaches the surface, it experiences a force barri

Question

When a molecule of a liquid approaches the surface, it experiences a force barrier that tries to keep it in the liquid. It thus has to do work to escape and loses some of its kinetic energy when it leaves. Assume that a water molecule can evaporate from the liquid if it hits the surface from the inside with a kinetic energy greater than the thermal energy corresponding to the temperature of boiling water, 100 oC.

(a) Use this to estimate the numerical value of the work 'W' required to remove a water molecule from the liquid.

(b) Even though the average speed of a molecule in water below the boiling point corresponds to a kinetic energy less than 'W', some molecules leave anyway and the water evaporates. Explain why this happens.

Explanation / Answer

The equivalence between average kinetic energy and thermal energy is found here:

http://en.wikipedia.org/wiki/Kinetic_theory#Temperature_and_kinetic_energy

In short Ek =3/2*(KT) or mV^2/2 =3/2 KT    (K is Boltzmann constant)

Therefore the work necessary to remove a water molecule from the liquid is

http://en.wikipedia.org/wiki/Kinetic_theory#Temperature_and_kinetic_energy

W =(3/2)* (KT) = 1.5*(1.38*10^-23)*(100+273)=7.72*10^-21 J

b)

The above relations gives only the average kinetic energy. In reality there is a distribution over all the possible energies. Thus some molecules will have smaller speeds and other molecules will have bigger speeds than the average kinetic energy. Therefore even if the average kinetic energy (speed) is less that that necessary for evaporation a small fraction of molecules will have a bigger energy than W(evaporation).

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.