Question

Answer in python code
1. Suppose someone, whose temperature is originally 37 ̊C, is murdered in a room
that has constant temperature 25 ̊C. The temperature is measured as 28 ̊C when the
body is found and at 27 ̊C 1 h later. How long ago was the murder committed from
discovery of the body? For the modeling of this question use Newton’s Law of
cooling. Newton’s Law of Heating and Cooling states that the rate of change of the
temperature (T) with respect to time (t) of an object is proportional to the
difference between the temperatures of the object and of its surroundings.
{ INITIALIZATION EQUATIONS }
temperature_of_object = 28
surrounding_temperature = 25
constant_of_proportionality = 0.33
temperature_change = constant_of_proportionality * (surrounding_temperature -
temperature_of_object)
{ RUNTIME EQUATIONS }
temperature_of_object(t) = temperature_of_object(t - dt) + (temperature_change) * dt
temperature_change = constant_of_proportionality * (surrounding_temperature -
temperature_of_object)
{ TIME SPECS }
STARTTIME=0
STOPTIME=4
DT=0.004

Answer 1

Here is the manual answer for your problem

from this method i get time duration as 3 hours

following is the implemention of this sollution in python code:

Raw:

temperature_of_object =t2= 28
surrounding_temperature = 25
constant_of_proportionality = 0.33
initial_bodytemparature=t1=37
temperature_after1hour=t3=27
# temperature_change = constant_of_proportionality * (temperature_of_object-surrounding_temperature)
# temperature_of_object(t) = temperature_of_object(t - dt) + (temperature_change) * dt
# temperature_change = constant_of_proportionality * (surrounding_temperature -temperature_of_object)
dT1=t2-t3 #change in temparature
dt1=1 #time change
temp=(((t2+t3)//2)-surrounding_temperature)
c=(dT1//dt1)*(1//temp) #calculation of constant_of_proportionality
print("time duration from murder commited to discovery of body")
dT=37-28
temp2=((37+28)//2)-25
dt=(1//(c*temp2))*dT
print(dt) # final time duration

End

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this is my first HomeworkLib please try to understand.please upvote me.

Thankyou :)