Answer:
The dude was killed around 6:30PM
Explanation:
Newton's law of cooling states:
where,
= initial temp
= temp of room
= temp after t hours
= how fast the temp is changing
= time (hours)
because the body was initlally 31ºC when the police found it
because that was the room temp
because the body temp drop to 30ºC after 1 hour
t = 1 because that's the time it took for the body temp to drop to 30ºC
we don't know k so we must solve for this
rearrange the equation to solve for k
plug in the numbers to solve for k
Now that we know the value for k, we can find the moment the murder occur. A crucial information that the question left out is the temperature of a human body when they're still alive. A living human body is about 37ºC. We can use that as out initial temperature to solve this problem because we can assume that the freshly killed body will be around 37ºC.
because the body was 37ºC right after being killed
because that was the room temp
because the body temp when the police found it
we solved this earlier
t = ??? we don't know how long it took from the time of the murder to when the police found the body
Rearrange the equation to solve for t
plug in the values
t ≈ 4.337 hours from the time the body was killed to when the police found it.
The police found the body at 11:00PM so subtract 4.337 from that.
11 - 4.33 = 6.66 ≈ 6:30PM