Question $1.(25$ points$)$ A house with a floor area of $100m^2$ and a ceiling height of $3m$ contains $12000$ moles of air. Heating

the house supplies an internal energy gain of $0\mathrm{.}1\frac{J}{s}$ per mole of air at a constant pressure of $1$ bar. This heating process

induces expansion of air that results with an unintended air leakage to the outdoors at a rate of $0\mathrm{.}04\frac{\text{m}\text{o}\text{l}}{s}.$ The leaking air

is assumed to have the same composition, temperature, pressure, and molar properties as the indoor air.

a$)$ Draw a simple sketch showing the system boundaries and flowing streams with their properties.

b$)$ Show the mass $($mole$)$ and energy balances. List all assumptions.

c$)$ Calculate the total rate of heat transfer to the air in the house in $kW.$