This must be solved using MatLab. 2. Newton\'s law of cooling gives the temperat

Question

This must be solved using MatLab.

2. Newton's law of cooling gives the temperature T(t of an object at time t in terms of To, its temperature at t-o, and Ts, the temperature of the surroundings. 0sJe A police officer arrives at a crime scene in a hotel room at 9:18 PM, where he finds a dead body. He immediately measures the body's temperature and find it to be 79.50F. Exactly one hour later he measures the temperature again, and find it to be 78.0°F. Determine the time of death, assuming that victim body temperature was normal (98.6°F) prior to death, and that the room temperature was constant at 69°F

Explanation / Answer

% matlab code start

k = log((78-69)/(79.5-69));

t = log((79.5-69)/(98.6-69)) / k;

d = 9.18 - t;

fprintf('Time of death = %.2f a.m ',d);

% matlab code end

% Explanation
T(t) = Ts +(T0 - Ts)e^kt

78 = 69 + (79.5 - 69)*e^k (t=1 hr)

9/10.5 = e^-k

-k = log (9/10.5)

Now, to determine t,

79.5 = 69 + (98.6 - 69)*e^-kt

= 10.5 / 29.6 = e^(-kt)

= log(10.5 / 29.6) = -kt

= t = log(10.5/29.6) / log(9/10.5)

%Output

Time of death = 2.46 a.m

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.