Python problem: Heat generated through the biological activity of microorganisms is often temperature dependent such that biological production is zero at temperature extremes (Tmin=15C; Tmax=30C) and maximized at an optimal temperature (Top=25C). Imagine a spherical lump of detritus in a lake that has a diameter of L=0.02 m and conductivity k=2W/m-K. As it moves through the water column, it loses heat by convection, h=3.1 W/m2-K, to the surrounding water (Twater=12C), and it generates heat through biological activity: Co(T - Tmax)(T - Tmin)? Q= (Tope I'min) {(Topt Tmin)(T Topt) - (Topy Imax)(Topt +Tmin 2T)} Lor] Imin T;T > Imax Where Co=0.008 K/s. The detritus has a density of 1000 kg/m?, and a heat capacity Cp=3500 J/kg-K. a) Plot Q as a function of T b) Plot dI as a function of T c) Solve for and plot the temperature as a function of time (over 10 hours) if the initial temperature of the detritus is 18,5C. Python problem: Heat generated through the biological activity of microorganisms is often temperature dependent such that biological production is zero at temperature extremes (Tmin=15C; Tmax=30C) and maximized at an optimal temperature (Top=25C). Imagine a spherical lump of detritus in a lake that has a diameter of L=0.02 m and conductivity k=2W/m-K. As it moves through the water column, it loses heat by convection, h=3.1 W/m2-K, to the surrounding water (Twater=12C), and it generates heat through biological activity: Co(T - Tmax)(T - Tmin)? Q= (Tope I'min) {(Topt Tmin)(T Topt) - (Topy Imax)(Topt +Tmin 2T)} Lor] Imin T;T > Imax Where Co=0.008 K/s. The detritus has a density of 1000 kg/m?, and a heat capacity Cp=3500 J/kg-K. a) Plot Q as a function of T b) Plot dI as a function of T c) Solve for and plot the temperature as a function of time (over 10 hours) if the initial temperature of the detritus is 18,5C