Final answer:
To find the rate of heat transfer due to radiation, the student must use the equation øA(T² - T¹), substituting T with the respective temperatures in Kelvin and applying the Stefan-Boltzmann constant and area of the body.
Step-by-step explanation:
The question asks for the instantaneous rate of change in the temperature of a room at a specific moment, but then proceeds to mention various mathematical rules typically used for finding derivatives in calculus.
However, based on the information provided and the subsequent details surrounding heat transfer, it is clear that the student is actually seeking to understand how to calculate the rate of heat transfer under different conditions such as conduction, convection, and radiation.
To find the rate of heat transfer due to radiation at a given temperature using the provided equation, one should first convert the temperature to Kelvin if necessary, and then insert the known values into the equation øA(T² - T¹), where ø is the Stefan-Boltzmann constant, A is the area of the radiating body, and T is the temperature in Kelvin.
To answer the specific question listed regarding the change in the rate of radiated heat by a body when the temperature changes from T₁ to 40°C, you would first convert 40°C to Kelvin and use the body’s initial temperature (T₁) also in Kelvin.
The difference of these temperatures to the fourth power is then multiplied by the Stefan-Boltzmann constant and the area of the body to determine the radiated heat's rate of change.