IGNOU MTE 8 2018 - Suppose the temperature of a body when discovered is o 85º F. Two

Question

Suppose the temperature of a body when discovered is o 85º F. Two hours later, the temperature is o 74º F and the room temperature is o 68º F. Find the time when the body was discovered after death (assume the body temperature to be o .698º F at the time of death.)

13 Feb 2018

Answer :

Word Count : 242

Let the temperature of the body at time $t$ be $T(t)$, room temperature $T_r = 68^\circ F$, and the normal body temperature at death $T_0 = 98.6^\circ F$. Newton’s law of cooling gives: $$ \frac{dT}{dt} = -k(T - T_r) $$ Step 1: Solve the differential equation $$ \frac{dT}{T - T_r} = -k \,

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