$($b$)$ A research team proposes to scale down the gas turbine of part $($a$),$ keeping all dimensions in the same proportions. The team assumes that the same hot and cold temperatures exist as in part $($a$)$ and that the net power output of the gas turbine is proportional to the overall volume of the device. Plot the ratio of the conduction through the shaft to the net power output of the turbine over the range $0\mathrm{.}005mL1m.$ Is a scaled$-$down device with $L=0\mathrm{.}005m$ feasible?