Answer:
(1/C)dR/dt - dT/dt = 0
Step-by-step explanation:
Let R be the rate at which the coffee cools down. Since R is proportional to the difference between the temperature of the coffee, T and the room temperature, we write
R = C(T - 18)
Where C is the proportionality constant.
To write a differential equation describing the derivative of the coffee temperature in terms of T and t, we need to differentiate
R = C(T - 18)
with respect to t.
Doing that, we have
dR/dt = CdT/dt
Or
(1/C)dR/dt - dT/dt = 0
Which is the required differential equation.
