In Calgary, the average temperature in January was $-5C,$ and the relative humidity on cold days is around $20\%.$ You inhale air at a rate of $5500m\frac{L}{m}in$ and exhale a saturated gas at body temperature. Assume the mass flow rates of the inhaled and exhaled air $($excluding water$)$ to be the same, and the heat capacity of air to be $1\mathrm{.}05\frac{J}{g.C}$ over the temperature range, and the specific enthalpy of water vapor at $-5C$ to be $2496\mathrm{.}2\frac{J}{g}($with reference to water at the triple point$).$ Water is ingested into the body as a liquid at $20C.$ If you would spend $8$ hours walking outside in these conditions, how much energy would you have lost by breathing?

Clearly indicate the assumptions you have made and construct the necessary process diagram and enthalpy tables required to do your calculation.