Question

mr. ratchett, an elderly american, was found murdered in his train compartment on the orient express at 7 am. when his body was discovered, the famous detective hercule poirot noted that ratchett had a body temperature of 28 degrees. the body had cooled to a temperature of 27 degrees one hour later. if the normal temperature of a human being is 37 degrees and the air temperature in the train is 22 degrees, estimate the time of ratchett's death using newton's law of cooling. a) write the initial value problem that models this scenario b) solve this equation using the method of separation of variables showing all the steps c) solve the differential equation using sage. copy and paste the sage code and show the plot of the solution curve.

Answer 1

Mr. Ratchett died approximately at 2AM.

Step-by-step explanation: Newton's Law of Cooling shows the cooling rate between a body and the environment, by stating that the rate is proportional to the difference in temperatures between them.

Mathematically, it is represented as:

This differential equation solved, gives the solution:

where

is temperature of the environment

is the initial temperature of the body

k is a parameter dependent of heat transfer coefficient, heat capacity and area of the body

t is time required to change the temperature

For the murder on the Orient Express, first determine parameter k.

In 1 hour, Mr. Ratchett's body decrease 1°:

k = 0.1823

Using the parameter, find estimate time:

0.1823t = 0.9163

t ≈ 5 hours

The body was found at 7AM. So, it took approximately 5 hours to cool down to 28° at that time. Therefore, Mr. Ratchett died at 2AM.

Explanation:

sorry if im wrong