$22\mathrm{.}14$ A runner and a cyclist are both training on a warm day. They can lose at most $1$ kg of moisture per hour via sweating without becoming dehydrated. A person looses most of their excess thermal energy via the evaporation of sweat and the latent heat of vaporisation of sweat is $2\mathrm{.}23106$ J kg$1.($a$)$ What is the maximum rate of heat transfer from the bodies of each athlete? $($b$)$ The runner runs with an efficiency of $10\%.$ What is the rate at which the runner can do work? $($c$)$ What is the change in internal energy of the runner over the course of $3$ hours training? $($d$)$ The cyclist cycles with an efficiency of $19\%.$ What is the rate at which the cyclist can do work? $($e$)$ What is the change in internal energy of the cyclist over the course of $3$ hours training?