9. Newton\'s Law of cooling/warming: The rate at which temperature changes in a
ID: 2880389 • Letter: 9
Question
9. Newton's Law of cooling/warming: The rate at which temperature changes in a cooling body is proportional to the difference between the temperature in the body and surrounding temperature. d' dt where T temperature, k proportional constant, t time and T surrounding temperature. TIME of DEATH: A murder was investigated at an apartment. When the police at 9am, the tempera- ture of the body was 78 Then when the forensics team got there at 10am, the temperature of the body was 76°F If the average body temperature is 98.6°Fand the room temperature was constant at 73°F, determine the time of death.Explanation / Answer
dT/dt = k( T - 73 )
=> dT/( T - 73 ) = k.dt
Integrating Both sides
=> loge| T - 73 | = kt + C
For t = 0 , T = 98.6 F
=> loge| 98.6 - 73 | = k(0) + C
=> C = loge( 25.6 )
Therefore , the equation becomes
=> loge| T - 73 | = kt + loge( 25.6 )
Let 9 am stuck m hours after the time of death , then 10 am struck m+1 hours after the death
=> loge| 78 - 73 | = km + loge( 25.6 )
and
=> loge| 76 - 73 | = k(m+1) + loge( 25.6 )
From above equations
=> loge( 3 ) - loge( 5 ) = k
=> loge( 3 ) = ( loge( 3 ) - loge( 5 ) )( m + 1 ) + loge( 25.6 )
=> m = 3.19709
which means approximately 3.2 hours before 9 am or 3 hours 12 minutes before 9 am
=> Death Time would be 05:48 am
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