Answer:
The temperature of the surrounding of the corpse is
T = (58+40e−t/2458+40e−t/24) ± ΔK
Where K is the temperature change of the corpse between 0 and t hours.
Step-by-step explanation:
A corpse loses or gains heat until it's temperature is in equilibrium with the temperature of its surrounding.
Since the temperature in degrees Fahrenheit of the corpse t hours after death is 58+40e−t/2458+40e−t/24,
let T be the temperature of the surrounding, then
T = (58+40e−t/2458+40e−t/24) ± ΔK
Where ΔK is the temperature change of the corpse between zero to t hours.
The temperature of the surroundings of the corpse is 58 °F
Since the temperature in degrees Fahrenheit of a corpse t hours after death is T = 58+40e−t/24.
The temperature of the surroundings is the temperature at which the corpse is in equilibrium with the surroundings and that is the steady state value of T at t = ∞.
So, substituting t = ∞ into the expression for T, we have
T = 58+40e−t/24.
T = 58+40e−∞/24.
T = 58+40e−∞
T = 58 + 40 × 0
T = 58 + 0
T = 58 °F
So, the temperature of the surroundings of the corpse is 58 °F
Learn more about Newton's law of cooling here:
https://brainly.com/question/9932355
