You detect the smell of gas in your house. Following the odor you discover a small gas leak in your furnace. Assuming a steady-state concentration profile of gas, diffusion of the gas through air, and radial diffusion, how much gas has leaked?

Data: You detect gas from your furnace.
Mole fraction detection limit for the nose is \(y_{\text {gas }}=1 \times 10^{-6}\)
Mole fraction of odor component in gas \(y_{\text {gas }, o}=1 \times 10^{-3}\) at \(r=0.1 \mathrm{~m}\)
\(T=25^{\circ} \mathrm{C} \quad P=1 \mathrm{~atm} \quad D_{\text {gas }}=6.55 \times 10^{-6} \mathrm{~m}^{2} / \mathrm{s}\)
Size of house \(\sim 20 \mathrm{~m}\) (equivalent diameter)