When discovered, the temperature of a body was 23 o C and the ambient temperatur

Question

When discovered, the temperature of a body was 23oC and the ambient temperature was a constant 20oC. The body was quickly taken to the morgue where the ambient temperature was maintained at 7oC. After 2 hours, the body temperature was found to be 19oC. Note that the normal living body temperature is 37oC and the formula for the cooling of a body is given by T(t) = TA + (T0 - TA)e-kt. Suppose that the decay rate k of the body was computed to be k=2. What equation can be used to correctly compute t, the amount of time that the body had been dead until it was discovered?

Which is correct from the options below?

19 = 18 + (37 - 18) e-4t

22 = 20 + (37 - 20) e-2t

23 = 20 + (37 - 20) e-2t

23 = 20 + (37 - 20) e-ln(2)t

22 = 20 + (37 - 20) e-4t

19 = 18 + (37 - 18) e-2t

21 = 20 + (37 - 20) e-2t

23 = 20 + (37 - 20) e-4t

21 = 20 + (37 - 20) e-4t

23 = 20 + (37 - 20) e-4t

19 = 18 + (37 - 18) e-4t

22 = 20 + (37 - 20) e-2t

23 = 20 + (37 - 20) e-2t

23 = 20 + (37 - 20) e-ln(2)t

22 = 20 + (37 - 20) e-4t

19 = 18 + (37 - 18) e-2t

21 = 20 + (37 - 20) e-2t

23 = 20 + (37 - 20) e-4t

21 = 20 + (37 - 20) e-4t

23 = 20 + (37 - 20) e-4t

Explanation / Answer

This problem pertains to Newtons Law of Cooling : Which states that the rate of change of temperature of an object is directly proportional to the difference between the temperature of the object and the surrounding.

Now we are given the formula for the cooling of the boday and it has been derived from the above stated law.

T(t) = TA + (T0 - TA)e-kt

Here T(t) = Temperature of the body at time 't'

TA = Temperature of the surrounding

T0 = Temperature of the body at initial condition

and k is decay constant

we are given that k = 2 (this value remains the same through out)

We need to find the equation that can be used to correctly compute t, the amount of time that the body had been dead until it was discovered.

We are given the living people have a body temperature of 37oC . So this is our initial temperature and

we know that when the dead body was discovered its temperature was recorded to be 23oC . And the temperature of the surrounding that is the ambiant temperature was 20oC.

=> T0 = 37 degree C

TA = 20 degree C

T(t) = 23 degree C

t = time taken for the body to reach from 37 degree C to 23 degree C

Plug the above date in the given formula :

T(t) = TA + (T0 - TA)e-kt

23 = 20 + (37 - 20)e-2t

Hence option C is correct

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

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