A long$-$distance runner performs work in the form of exercise with an average power output of $650$ W$.$ In $35.$ minutes of running, her body loses $5\mathrm{.}2$ x $10^5$ J of heat. $($a$)$ What was the change in the internal energy of the runner? $($b$)$ How many calories would the runner have to ingest to replace the energy lost in part $($a$)?$