Engineering Board Exam Reviewer · Applications: Cooling, Heating, and Mixture Problems · easy

Newton's law of cooling states that the rate of change of an object's temperature T is proportional to the difference between T and the ambient temperature Ts. Which equation expresses this?

  1. dT/dt=kT
  2. dT/dt=kTs
  3. dT/dt=k(T-Ts)2
  4. dT/dt=k(T-Ts)

Answer

D. dT/dt=k(T-Ts)

Solution

The rate of change is proportional to the temperature difference: dT/dt=k(T-Ts), with k<0 for an object cooling toward Ts.

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