2. A waste heat pond from a nuclear reactor was found to cool overnight like a mixed batch reactor(MBR) (no flows). a. If the heat loss approximately were to be

found to approximately follow a second order decay reaction rate (r = -kT²), integrate the differential equation d T / d t=-k T^{2} as subject to the initial condition that at t = 0 then T= 40 °C. p. If t = 0 is at 10 pm, and k = 5 x 105 (°C-hour), then what will be the temperature by 3 am? c. Explain why k has to have the units of (°C-time)1