In: Advanced Math
A body was found at 2pm in a room kept at 70 degrees. the student took the temp of the body and it was 80 degrees and then called the police 1 hour later the body was 75 degrees. Using newtons law of cooling determine the time of death. I know it is a Diff Q please show all steps. I will rate
denotes the time since death (in hour). Let
when the body was
found. Let
be the body
temperature at time
. Let
be the room
temperature. By Newton's law, we have
for some constant . We solve this. First,
let
; then the above equation becomes
Separation of variables give
This implies
, where
is a constant (of
integration).
Recall that in one hour the temperature drops from to
. Thus,
These give
Hence, . Thus,
Since , we
get
Therefore,
. We solve
to get
Hence,
Thus, after approximately hours (
minutes) since death the body temperature would fall to
degree. It
has been given that this happened at 2 pm. Hence, the time of death
is (
) approximately
pm.