[Physics] Is the integral of temperature over time useful

temperaturethermodynamics

Just a hypothetical question. Suppose I have an oven that heats food, and I can measure the temperature (over time) accurately at the surface of the food being heated (this may or may not be feasible). Is the integral of the temperature measurement (wrt time) useful in controlling the cooking time? (The actual heat transfer function is unknown, as is the heat capacity of the food, as is the nature of cooking. It is assumed that such issues are too complex to calculate. The oven may contain a heating element that turns on and off with some duty cycle.)

Best Answer

Yes, the integral is useful for control, for example in a PID controller. It is then the difference between the measured temperature and the setpoint. The power to the heater is primarily proportional to this difference. Adding a term proportional to the integral will make it reach the setpoint sooner.