At 7: 00 pm the police discovered a body in a hotel room which maintained a constant temperature of 24 degree c. at the time of discovery, the temperature of the dead body was 36 degree c. after 4 hours the temperature of the body fell to 30 degree c. use newton’s law of cooling to approximate the time of death. using the formula: t – tr = (to – tr)e–t/tau

Explanation:

According to Newton's law of cooling,

T(t) is the temperature at time t

is temperature of surrounding

At the time of discovery, the temperature of the dead body was,

Temperature of the surrounding,

Temperature after 4 hours,

So,

On solving the above equation,

k = 0.1735

Now, put the value of k in equation (1) at T = 36 degrees C

We know that, the temperature of body before death is T(t) = 37 degrees C

On solving above equation,

t = -0.46 hour

As time can't be negative and we have taken 7:00 pm as reference time.

So, t = 27.67 minutes

So, the death of the person is at 6 : 32 pm. Hence, this is the required solution.

c

explanation: