Question

Cooling: The body of an apparent victim of a crime is discovered by detectives at 9...

Cooling:

The body of an apparent victim of a crime is discovered by detectives at 9 AM, at which time the body temperature was measured to be 88°. Two hours later the temperature was 82°. Using Newton’s Law of Cooling, determine the time of death if the room temperature was a constant 75°.

Homework Answers

Answer #1

where:

k: the constant of proportionality

T: the temperature of the surrounding enviroment (constant)

Ts: the temperature of the object at time t

T(0)= 88

T(1)=82

to determine C and, we substitute the initial conditions to arrive at the system of equations

the first equation tells us , so the second equation becomes:

thus,

the solution is:

assuming the boby temperature was last 98.6

that is, the ime of death was approximately 58 minutes before 9:00, or 8:02

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
This exercise uses Newton's Law of Cooling. Newton's Law of Cooling is used in homicide investigations...
This exercise uses Newton's Law of Cooling. Newton's Law of Cooling is used in homicide investigations to determine the time of death. The normal body temperature is 98.6°F. Immediately following death, the body begins to cool. It has been determined experimentally that the constant in Newton's Law of Cooling is approximately k = 0.1947, assuming time is measured in hours. Suppose that the temperature of the surroundings is 55°F. (a) Find a function T(t) that models the temperature  t hours after...
If the temperature difference DT between an object and it surroundings is not too great, the...
If the temperature difference DT between an object and it surroundings is not too great, the rate of cooling or warming obeys Newton’s Law of Cooling, d(DT)/dt = – K DT where K is a constant. (a) Why is there a minus sign on the right-hand side of the equation? (b) On what factors does K depend and what are its units? (c) It DTo is the temperature difference at time to, what is the temperature difference at time t...
In room Q-666 a student, at 8:00 AM, finds the murdered body of Mr. Jones. The...
In room Q-666 a student, at 8:00 AM, finds the murdered body of Mr. Jones. The student takes the temperature of the body: 90 F. Two hours later, the police determines the new temperature: 80 F. The temperature of the room is constant 70 F. The normal temperature of the living human being is 98.6 F. Determine the time approximate death
A detective is called to the scene of a crime where a dead body has just...
A detective is called to the scene of a crime where a dead body has just been found. She arrives on the scene at 10:23PM and begins her investigation. Immediately, the temperature of the body is taken and found to be 80℉. The detective checks the thermostat and finds that the room has been kept at a constant 68℉. After the evidence from the crime scene is collected, the temperature of the body is taken once more exactly one hour...
A body was found in the basement of the Underwater Basket Weaving Building at​ 12:00 noon​...
A body was found in the basement of the Underwater Basket Weaving Building at​ 12:00 noon​ today, where the temperature is a steady 65 degrees Fahrenheit. When​ found, the core temperature was 91.1 degrees Fahrenheit.  Two hours​ later, at​ 2:00 PM, the core temperature had fallen to 88.4.   Assuming that the body temperature was 98.6 at the time of​ death, use​ Newton's law of cooling to find the time of death.   ROUND TO 2 DECIMAL PLACES. The time of death...
When a murder is committed, the body, originally at 37 degree Celsius, cools according to Newton’s...
When a murder is committed, the body, originally at 37 degree Celsius, cools according to Newton’s Law of Cooling. Suppose that after two hours the temperature is 35 degree Celsius, and that the temperature of the surrounding air is constant at 20 degree Celsius. Find the temperature, H, of the body as a function of t, the time in hours since the murder was committed.
Use Newton's law of cooling model to partially solve a murder mystery. At 3:00 p.m. a...
Use Newton's law of cooling model to partially solve a murder mystery. At 3:00 p.m. a deceased body is found. Its temperature is 70+ F. An hour later the body temperature has decreased to 60+ . It's been a winter inversion in SLC, with constant ambient temperature 30+ . Assuming the Newton's law model, estimate the time of death
police arrive at a murder scene at 1:30 am and immediately record the body's temperature which...
police arrive at a murder scene at 1:30 am and immediately record the body's temperature which was 93 degrees Fahrenheit. at 2:00 am, after thoroughly inspecting and fingerprinting the area, they again took the temperature of the body which had dropped to 83 degrees F. the temperature of the crime scene has remained at a constant 70 degrees F. Determine when the person was murdered. (assume that the victim was healthy at the time of death. that is, assume that...
In 1701, Issac Newton proved his Law of Cooling: T(t) =Aekt +Ta, which is an exponential...
In 1701, Issac Newton proved his Law of Cooling: T(t) =Aekt +Ta, which is an exponential model that relates the temperature of an object T as a function of time t (we will use minutes) that is placed in an environment with ambient temperature Ta. Suppose a cup of hot coffee is served at 160◦F and placed in a room with an ambient temperature 75◦. After 5 minutes, the cup of coffee has a temperature of 131◦F. a) Create a...
Newton’s Law of Cooling tells us that the time rate of chnge in temperature T(t) of...
Newton’s Law of Cooling tells us that the time rate of chnge in temperature T(t) of a body immersed in a medium of constant temperature A is proportional to the difference A − T.The DE modeling this is dT dt = k(A − T). A cup of hot chocolate is initially 170◦ F and is left in a room with an ambient temperature of 70◦ F. Suppose that at time t = 0 it is cooling at a rate of...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT