Question

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

Answer 1

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.