For a postmortem report, a doctor requires to know approximately the time of death of the deceased. He records the first temperature at 10 · 00   am to be 93 · 4   ° F . After 2 hours he finds the temperature to be 91 · 4   ° F . If the room temperature (which is constant) is 72   ° F estimate the time of death. (Assume normal temperature of a human body to be 98 &#18

Step-by-step solution

Let T be the temperature of the body at any time t . By Newton's law of cooling d T d t ∝ T - 72 since, S = 72   ° F d T d t = k T - 72 ⇒ ∫ d T T - 72 = ∫ k d t ⇒ ln T - 72 = k t + c or T = 72 + c e k t At t = 0 ,   T = 93 · 4 ⇒ c = 21 · 4 [First recorded time 10   am is t = 0 ] ∴   T = 72 + 21 · 4 e k t When t = 120 ,   T = 91 · 4 ⇒ e 120 k = 19 · 4 21 · 4 ⇒ k = 1 120 log e 19 · 4 21 · 4