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Newton's law of cooling leads to a differential equation stating that the rate of temperature fall is proportional to

  • A.the body's absolute temperature
  • B.the fourth power of the body's absolute temperature
  • C.the elapsed time since cooling began
  • D.the excess of the body's temperature over its surroundings

Answer: D

The law gives \( d\theta/dt = -k(\theta - \theta_{s}) \), whose solution is an exponential decay towards the surrounding temperature. The fourth power belongs to radiative transfer by Stefan's law, which the cooling law approximates for a small excess, and proportionality to elapsed time would give a straight-line fall rather than an exponential one

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