What is the Time of Death Based on Newton's Law of Cooling?

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SUMMARY

The discussion focuses on determining the time of death using Newton's Law of Cooling, specifically in a murder case where the victim's body temperature was recorded at 88 degrees Fahrenheit at 4:30 AM and later at 85.8 degrees after two hours. The standard body temperature of 98.6 degrees is used as the initial temperature (T0), while the surrounding temperature is set at 76 degrees (Tm). The equation T = (T0-Tm)e^(-kt) + Tm is employed to solve for time (t), with an emphasis on the application of logarithms to isolate the variable.

PREREQUISITES
  • Understanding of Newton's Law of Cooling
  • Basic knowledge of logarithmic functions
  • Familiarity with temperature measurement in Fahrenheit
  • Ability to manipulate exponential equations
NEXT STEPS
  • Study the application of Newton's Law of Cooling in forensic science
  • Learn how to solve exponential equations using logarithms
  • Explore temperature conversion between Celsius and Fahrenheit
  • Investigate case studies involving time of death estimation
USEFUL FOR

Students in forensic science, criminal investigators, and anyone interested in the mathematical applications of physics in real-world scenarios.

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Homework Statement


A man was murdered and inspectors found his body temperature to be 88 degrees at 4:30AM.
Climate control in the room was set to 76 degrees.

Temperature of his body was taken again 2 hours later and found to be 85.8 degrees.

The standard body temperature for human beings is 98.6 degrees.

Need to find the time at which the man was killed (so when his temperature was 98.6)


Homework Equations



T = (T0-Tm)e^(-kt) + Tm

Where T0 = Initial temperature of the body (failry sure this is 98.6 degrees)
and Tm = Temperature of the surrounding medium (76 deg
rees)


I missed the lesson and this is catchup work and I'm having trouble grasping how to use logs/natural logs to solve for t.

Thank you very much.
 
Physics news on Phys.org
Wow, pretty specific example there.

Thanks.
 

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