Given the information in a$.)$ as well as the provided solution of $92$ mins for the pressure drop. Solve b$.)$ and c$.),$ in the attached image.

a$.)$ Furnace given in the figure has volume $0\mathrm{.}283$ m$3$ and contains air, which may be consider an ideal gas. The vacuum pump is pumping air out. During the pump$-$out process, the heating coil in the tank hold temperature in the tank constant. The volumetric flow rate at the inlet of the pump, independent of pressure is $4\mathrm{.}7210-4$m$3/$s$.$ How long does it take the pressure to fall from $1$ to $0\mathrm{.}0001$atm? SA lake has surface area of $100k{m}^2.$ One river is bringing water into the lake at the rate of $1000\frac{m^3}{s},$ while another is taking water out at $8000\frac{m^3}{s}.$ Evaporation and seepage are negligible. How fast is the level of the lake rising or falling? SOLUTION TO a$.)$ IS $92$ MINS.