Density of water at $4^\circ$C and $20^\circ$C are $1000\,\text{kg/m}^3$ and $998\,\text{kg/m}^3$ respectively. The increase in internal energy of $4\,\text{kg}$ of water when it is heated from $4^\circ$C to $20^\circ$C is ___ J.
(Specific heat capacity of water $= 4.2\,\text{J g}^{-1}\text{K}^{-1}$ and atmospheric pressure $=10^5\,\text{Pa}$)