# Question 45474

May 14, 2014

Your body loses 6.8 kJ of heat when 2.8 g of sweat evaporates from your skin at 25 °C.

This is a problem that involves phase changes. The sweat is changing from the liquid phase to the gaseous phase.

It takes energy to separate the liquid molecules from each other and get them into the gas phase. The sweat is evaporating. The energy required is the enthalpy of vaporization ΔH_"vap" or the heat of evaporation.

The enthalpy of vaporization of water varies with temperature. At 25 °C, ΔH_"vap" = 2441 J/g.

The mass $m$ of the sweat is 2.8 g. The heat $q$ required to evaporate this sweat is

q = mΔH_"vap"# = 2.8 g × $\left(2441 \text{ J")/(1" g}\right)$ = 6800 J = 6.8 kJ