A rigid container with volume V is originally filled with water of Temperature T1. A hose is then connected to an inlet port and hotter water of temperature T2 is pumped into the container at mass flow rate m in., while another venting port allows the displaced water to flow out , the pressure being constant. Assuming the incoming hot water mixes quickly with the inside water and temperature is a good approximation uniform, derive an expression for the temperature T inside the container as a function of time. Neglect effects of gravity and kinetic energy