Question

2. A coroner uses a formula, derived from Newton's Law of Cooling, to calculate the elapsed time since a person died. The formula is t = -10 ln ((T-R)/ (37-R))

where t is the time in hours since the death, T is the body's temperature measured in C and R is the constant room temperature in C.

An accountant stayed late at work one evening and was found dead in his office the next morning. The officece temperature was constant at 21C

(a) At 10 am the coroner measured the body temperature. The temperature of the body was found to be 29.7C. Determine the accountant's estimated time of death, leave your answer

correct to the nearest minute.

(b) What would the temperature of the body be at 10am, if the accountant had died at 2am?

(c) Sketch graphs of t versus T for R = 18; 21; 24 on the same axes, clearly showing the vertical asymptote for each graph.

(d) If the constant oce temperature had been less than 21C, would the time of death found in (a) be earlier or later. Give reasons for your answer.

Answer 1

Given equation, t = -10 ln ((T-R)/(37-R))

a) Here given R = 21 C and T = 29.7 C

Putting this values in the above equation we get, t = -10 ln ((29.7-21)/(37-21))

i.e., t = -10 ln (8.7/16)

i.e., t = 6.092656966 h

i.e., t 366 mins

Therefore, accountant's estimated time of death is = 10:00 am - 366 min = 3:56 am

b) If the accountant had died at 2 am, then the body temperature at 10 am will be = 21+(37-21)*e^-8/10 28.19 C

c) Here, X-axis denotes T and Y-axis denotes t.

For R = 18 :

For R = 21 :

For R = 24 :

d) Let, the constant oce temperature be 20 C, then the time since death will be = -10 ln ((29.7-20)/(37-20)) 337 mins.

Therefore, the time of death will be later.