A copper block of unknown mass at $90$ degree C is put into an insulated tank containing $0\mathrm{.}05$ m$^3$ of water at $18$ degree C$.$ A paddle mixer, driven by a $150$ W motor, is started at the same time to stir the water. Thermal equilibrium is established after quarter of an hour, the final temperature being $20\mathrm{.}5$ degree C$.$ Determine the mass of the copper block. $($Answer: $14\mathrm{.}8$ kg$)$