Q. 18 - Calculus

Question

Suppose an object is heating up according to a model for Newton’s Law of Cooling with temperature satisfying $\frac{dT}{dt}=k(350-T)$ for some constant $k$.

(a) What is the ambient temperature of the environment under this model? 

(b) Given that the temperature T(t) is increasing and that $0<T<350$, is the constant $k$ positive or negative, and why?

(c) Use the differential equation to argue that the object’s temperature changes are faster when it is much cooler than the ambient temperature than when it is close to the ambient temperature. 

(d) Part (c) is the basis for the oft-misunderstood saying “Coldwater boils faster.” Why? 

Step-by-Step Solution

Answer

Ans:  

Step 1. Given information.

given,

       $\frac{dT}{dt}=k(350-T)$

Step 2.