Application Newton’s Law of cooling using first-order differential equations

Newton's Law of Cooling describes how the temperature of an object changes over time when it is exposed to a surrounding medium with a different temperature. The rate at which the temperature of the object decreases is proportional to the difference between its temperature and the constant temperature of its surroundings. By applying first-order differential equations, we can calculate how much an object’s temperature decreases over time relative to the surrounding environment. This study aims to analyze the principles governing the rate of temperature change, solve the differential equation using mathematical methods, and validate the theoretical model to predict future temperature changes. The findings provide a quantitative foundation for understanding temperature variations in objects exposed to different thermal conditions, offering accurate predictions and practical solutions to real-world cooling problems.