Determine time of death
INTRODUCTION
INTRODUCTION
In this article, I have discussed how to determine the time of death of a murdered person.it can be determined with the help of differential equation.
In this article, I have discussed how to determine the time of death of a murdered person.it can be determined with the help of differential equation.
The estimation of time of death is based on the temperature of the body at two times
The estimation of time of death is based on the temperature of the body at two times
1)when the victim is found and
1)when the victim is found and
2)then a few hours later.
2)then a few hours later.
Problem Statement
Problem Statement
Suppose that you come into your professor's office to ask some questions shortly before 9:00 a.m. on Friday. You and him lying on the door of his office, dead.
Suppose that you come into your professor's office to ask some questions shortly before 9:00 a.m. on Friday. You and him lying on the door of his office, dead.
You quickly call the police and their investigators take several measurements over the next hour, including:
You quickly call the police and their investigators take several measurements over the next hour, including:
1) the body temperature at 9:00 a.m. - 80 degrees
1) the body temperature at 9:00 a.m. - 80 degrees
2)the body temperature at 10:00 a.m. - 78 degrees
2)the body temperature at 10:00 a.m. - 78 degrees
3)room temperature - 70 degrees (constant)
3)room temperature - 70 degrees (constant)
You quickly realize that the police believe you to be a prime suspect. You know that you were studying until midnight, but you aren't sure if that is enough information. You need to know the time of death!
You quickly realize that the police believe you to be a prime suspect. You know that you were studying until midnight, but you aren't sure if that is enough information. You need to know the time of death!
Solution:
Solution:
According to Newton's law of cooling,the difference between body temperature and room temperature changes at a rate pro- portional to that difference.
According to Newton's law of cooling,the difference between body temperature and room temperature changes at a rate pro- portional to that difference.
Suppose, T(t) is the body temperaturse at time t, k is a constant,
Suppose, T(t) is the body temperaturse at time t, k is a constant,
Constant K and A can be determined by the information that we have noted at beginning of the problem Statement.
Constant K and A can be determined by the information that we have noted at beginning of the problem Statement.
At t = 9, T = 80 and at t = 10, T = 78. so,
At t = 9, T = 80 and at t = 10, T = 78. so,
Normal temperature of human body is 98.6 F, Now we just need to determine t when T=98.6
Normal temperature of human body is 98.6 F, Now we just need to determine t when T=98.6
This corresponds to 4:17 a.m.,The professor died at bit before 4:17 a.m.,so somehow you can prove that you were in bed at that time.
This corresponds to 4:17 a.m.,The professor died at bit before 4:17 a.m.,so somehow you can prove that you were in bed at that time.
Conclusion and Application
Conclusion and Application
finding out the time of murder in such cases which is of lot of importance in determining the path that has to be taken by the police or detective to solve the case.
finding out the time of murder in such cases which is of lot of importance in determining the path that has to be taken by the police or detective to solve the case.
By useing first order differential equations and newton's law of cooling we can save our self. calculus can be useful in many di- erent and surprising way just like this.we can solve murder mystery by using calculus.
By useing first order differential equations and newton's law of cooling we can save our self. calculus can be useful in many di- erent and surprising way just like this.we can solve murder mystery by using calculus.
REFERENCES
REFERENCES
Applications of First Order Di rential Equations in RealWorld,
faculty.kfupm.edu.sa/math/ahasan/coursecontents/chapter4.doc8