Newton’s Law of Cooling. h is law states that the change in
temperature of an object over time t, denoted T´, varies directly with the dif erence between
the temperature of the object T and the temperature of the surrounding environment, or
ambient temperature, A. Letting -k represent the constant of variation for a positive value of
k, write an equation to represent Newton’s Law of Cooling.

Question

Newton’s Law of Cooling. h is law states that the change in 
temperature of an object over time t, denoted T´, varies directly with the dif erence between 
the temperature of the object T and the temperature of the surrounding environment, or 
ambient temperature, A. Letting -k represent the constant of variation for a positive value of 
k, write an equation to represent Newton’s Law of Cooling.

anonymous · Answer

OK. We need some variables here.

T(t) = temperature of the item at time t.
T_0 = temperature of the item at time t=0
T_1 = temperature of the surroundings
k  = constant of variation (reflects the heat transfer characteristics of the object and surroundings)

anonymous · Answer

Given the stuff above, we will get the following equation:$$T(t)=T_1 +(T_0-T_1)e^{-kt}$$Note that at t=0, the value of the function is T_0, and after a very long time, the value approaches T_1.

anonymous · Answer

By the way, the equation works for either heating or cooling.