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.

Answer 1

Time of Death = 2 : 49 : 45 AM

Explanation:

The formula for Newton's Law of Cooling is written as follows:

dT/dt = - K(T - Ts)

where,

dT = change in temperature

dt = time interval

K = cooling constant

T = Final Temperature of object

Ts = Surrounding Temperature

First, we will use the data of cooling of body from 28°C to 27°C to find the cooling constant of the body:

dT = 27°C - 28°C = -1°C

dt = 1 hr = 3600 s

K = ?

T = 27°C

Ts = 22°C

Therefore,

-1 °C/3600 s = - K(27 °C - 22 °C)

K = 1 °C/(3600 s)(5 °C)

K = 5.55 x 10⁻⁵ /s

Now, we use data for cooling of body from 37 °C to 28 °C to find the time of death:

dT = 28°C - 37°C = -5°C

dt = ?

K = 5.55 x 10⁻⁵ /s

T = 28°C

Ts = 22°C

Therefore,

- 5 °C/dt = - (5.55 x 10⁻⁵ /s)(28 °C - 22 °C)

dt = 5 °C/(5.55 x 10⁻⁵ /s)(6 °C)

dt = 1.5 x 10⁴ s

dt = 4.17 h = 4 h 10 min 15 s

Therefor,

Time of Death = 7 : 00 : 00 AM - 4 : 10 : 15

Time of Death = 2 : 49 : 45 AM