Question

You have two cups full of liquid. Cup A ls 100 degrees C. Cup B is 20 degrees C. What is the difference in the kinetic energy of the molecules in each cup?

Answer 1

The average kinetic energy of the molecules in Cup A is 27 % greater than that of the molecules in Cup B.

Explanation:

There is a distribution of kinetic energies among the molecules in each cup

All we can talk about are the average kinetic energies of the molecules.

Per Kinetic Molecular Theory, the average kinetic energy of the molecules is directly proportional to the temperature.

`color(blue)(bar(ul(|color(white)(a/a)KE ∝ Tcolor(white)(a/a)|)))" "`

The relative kinetic energies of the molecules in Cups A and B are

`(KE_"A")/(KE_"B") = T_"A"/T_"B"`

`T_"A" = "(100 + 273.15) K = 373.15 K"`
`T_"B" = "(20 + 273.15) K = 293.15 K"`

∴ `(KE_"A")/(KE_"B") = (373.15 color(red)(cancel(color(black)("K"))))/(293.15 color(red)(cancel(color(black)("K")))) = 1.27`

The average kinetic energy of the molecules in Cup A is 27 % greater than that of the molecules in Cup B.