Question

A murder victim is discovered and a lieutenant from the Forensic science laboratory is summoned to estimate the time of death. The body is located in a room that is kept at a constant temperature of 680F. The lieutenant arrived at 9.40P.M. and measured the body temperature as 94.40F at that time. Another measurement of the body temperature at 11PM is 89.20F. Find the estimated time of death.​

Answer 1

Answer:

9 o-clock or 8:50

Step-by-step explanation:

Answer 2

The estimated time of death is 7:50 PM (9:40 PM - 110 minutes).

To find,

The estimated time of death.

Given,

A constant temperature of 680F

The Lieutenant arrived at 9.40P.M

After the lieutenant arrived the body temperature is 94.40F

Another measurement of the body temperature at 11 PM is 89.20F

Solution,

To estimate the time of death, we can use Newton's law of cooling, which states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. The law can be expressed as:

T(t) = T0 + (T1 - T0) * e^(-kt)

where T(t) is the temperature of the body at time t, T0 is the temperature of the surroundings, T1 is the initial temperature of the body, and k is the cooling constant.

We can use the given measurements of the body temperature to find the cooling constant k. Let's first convert the temperatures from Fahrenheit to Celsius, as the law of cooling requires the use of the Celsius scale:

Initial temperature: T1 = (94.4 - 32) * 5/9 = 34.7 °C

Temperature at 11PM: T(11) = (89.2 - 32) * 5/9 = 31.8 °C

Surrounding temperature: T0 = 68 °F = 20 °C

Substituting these values into the law of cooling, we get:

T(11) = T0 + (T1 - T0) * e^(-k * 1.5)

Solving for k, we get:

k = ln((T(11) - T0) / (T1 - T0)) / (-1.5) = 0.104 min^-1

Now, we can use the law of cooling to find the time t since death when the body temperature was 94.4 °F:

94.4 = 20 + (34.7 - 20) * e^(-0.104t)

Solving for t, we get:

t = -ln((94.4 - 20) / (34.7 - 20)) / 0.104 = 110 minutes

Therefore, the estimated time of death is 9:40 PM - 110 minutes = 7:50 PM.

For further reference,

https://brainly.in/question/9179406?referrer=searchResults

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