He does some investigation and apply newtons law of cooling,He takes notes of temprature for some times.

Then he applies the equations

If θ(t) is temperature of corpse at time t and Su be the Surrounding temperature.

Then According to Newton’s Law of cooling

dθ(t) dt = −k(θ(t) − Su)

This is a first order linear differential equation.

The solution, under the initial condition θ(0) = θ0, is given by

θ(t) = Su + (θ0 − Su)e −kt

Thus,

θ(t1)−Su θ(t2)−Su = e −k(t1−t2)

⇒ k(t1 − t2) = −ln( θ(t1)−Su θ(t2)−Su)

Putting the given values in the above equations.We get k as

k = (−1/2)(−ln35−28 34−28)

⇒ k = 0.074 4

Supposing initial temperature to be normal body temperature i.e. 37.0 ◦C

(t − t1) = (1/k)(−ln37−28 35−28) =

(t − t1) = −3.38

Converting Decimal into Minutes

t = 18 : 00 − 3 : 22

T = 14 : 38

Thus he can predict that the death has been occurred at 2:38,When he was not in room,he was in lab

Hence He can prove himself innocent by "APPLIED MATHEMATICS"