Show that the specific heat capacity of water in terms of universal gas constant.

Explanation

An oscillation of a molecule in one dimension has average energy `2xx(1)/(2)K_(B)T=K_(B)T.`
In three dimensions, the average energy is 3KT per atom.
Hence spccific heat capacity of water (assumed to behave as solid),
`C=(("no of atoms in water molecule")N_(0))/("rise in temperature")xx3KDeltaT` and no of atoms in a water molecule = 3
`i.e.C=9K_(B)N_(A)=9R " " "where" R=8.314J " " "mole"^(-1)K^(-1)`
Note : For solids U = 3RT, at constant pressure `(DeltaQ)/(DeltaT)=3R` = 3R.