Question

In a murder investigation, the temperature of the corpse was 35°C at 1:30 pm and 24°C 2 hours later. Normal body temperature is 37°C, and the surrounding temperature was 5°C. How long ago did the murder occur? Assume the body's temperature obeys Newton's Law of Cooling, where the rate of change of temperature is proportional to the difference between the body's temperature and the ambient temperature.

Answer 1

To determine how long ago the murder occurred, we can use Newton's Law of Cooling. The murder occurred approximately 1.27 hours ago.

Step-by-step explanation:

To determine how long ago the murder occurred, we can use Newton's Law of Cooling. According to this law, the rate of change of temperature is proportional to the difference between the body's temperature and the ambient temperature. In this case, the body's temperature dropped from 35°C to 24°C over a span of 2 hours, with an ambient temperature of 5°C.

We can set up an equation where the rate of change of temperature (dT/dt) is equal to a constant (k) multiplied by the difference between the body's temperature (T) and the ambient temperature (A). This can be written as dT/dt = -k(T - A).

Substituting the given values into the equation, we have dT/dt = -k(35 - 5) and dT/dt = -k(24 - 5), where k is the constant we need to find.

Since the rate of change of temperature is equal to the difference between the two temperatures divided by the time elapsed, we can write the equation as (35 - 5)/2 = (24 - 5)/t, where t is the time elapsed since the murder.

Simplifying and solving for t, we have t = (24 - 5)*(2)/(35 - 5). Plugging in the values, we get t = 19*(2)/30 = 38/30 = 1.27 hours.

Therefore, the murder occurred approximately 1.27 hours ago.