Question

In a murder investigation the temperature of the corpse was 32.5 C at 1:30 pm and 30.3 C an hour later. Normally body temperature is 37 C and the temperature of the surrounding is 20 C. When did the murder take place? What I did is using y(t)=y(0).e^kt and y(t)=T(t)-Tsurrounding = T(t)-20

t=0 T=37
t1=? T=32.5

Answer 1

To determine when the murder took place, we can use Newton's Law of Cooling to calculate the time interval between the two temperature measurements of the corpse.

Step-by-step explanation:

To determine when the murder took place, we can use Newton's Law of Cooling. The formula is given as T(t) = T_surrounding + (T_initial - T_surrounding) * e^(-kt), where T(t) is the temperature of the corpse at time t, T_initial is the initial temperature of the corpse, T_surrounding is the temperature of the surrounding environment, and k is the cooling constant.

By plugging in the given values into the formula, we can solve for k. First, let's convert the temperature values to Kelvin by adding 273.15. So, T_initial = 37 + 273.15 = 310.15 K, T_1 = 32.5 + 273.15 = 305.65 K, and T_surrounding = 20 + 273.15 = 293.15 K.

Now, let's plug in these values into the formula and solve for k:

305.65 = 293.15 + (310.15 - 293.15) * e^(-k).

From here, we can solve for k and find the time interval between the two temperature measurements, which will give us an estimate of when the murder took place.