1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
PolarNik [594]
3 years ago
5

A rich industrialist was found murdered in his house. The police arrived at the scene at 11:00 PM. The temperature of the corpse

at that time was 31ºC and one hour later it was 30ºC. The temperature of the room in which the body was found was 22ºC. Estimate the time the murder occurred
Engineering
1 answer:
d1i1m1o1n [39]3 years ago
7 0

Answer:

The dude was killed around 6:30PM

Explanation:

Newton's law of cooling states:

    T = T_m + (T_0-T_m)e^{kt}

where,

T_0 = initial temp

T_m = temp of room

T = temp after t hours

k = how fast the temp is changing

t = time (hours)

T_0 = 31     because the body was initlally 31ºC when the police found it

T_m = 22   because that was the room temp

T = 30  because the body temp drop to 30ºC after 1 hour

t = 1 because that's the time it took for the body temp to drop to 30ºC

k=???   we don't know k so we must solve for this

rearrange the equation to solve for k

T = T_m + (T_0-T_m)e^{kt}

T - T_m= (T_0-T_m)e^{kt}

\frac{T - T_m}{(T_0-T_m)}= e^{kt}

ln(\frac{T - T_m}{T_0-T_m})=kt

\frac{ln(\frac{T - T_m}{T_0-T_m})}{t}=k

plug in the numbers to solve for k

k = \frac{ln(\frac{T - T_m}{T_0-T_m})}{t}

k = \frac{ln(\frac{30 - 22}{31-22})}{1}

k=ln(\frac{8}{9})

Now that we know the value for k, we can find the moment the murder occur. A crucial information that the question left out is the temperature of a human body when they're still alive. A living human body is about 37ºC. We can use that as out initial temperature to solve this problem because we can assume that the freshly killed body will be around 37ºC.

T_0 = 37     because the body was 37ºC right after being killed

T_m = 22   because that was the room temp

T = 31  because the body temp when the police found it

k=ln(\frac{8}{9})   we solved this earlier

t = ???   we don't know how long it took from the time of the murder to when the police found the body

Rearrange the equation to solve for t

T = T_m + (T_0-T_m)e^{kt}

T - T_m= (T_0-T_m)e^{kt}

\frac{T - T_m}{(T_0-T_m)}= e^{kt}

ln(\frac{T - T_m}{T_0-T_m})=kt

\frac{ln(\frac{T - T_m}{T_0-T_m})}{k}=t

plug in the values

t=\frac{ln(\frac{T - T_m}{T_0-T_m})}{k}

t=\frac{ln(\frac{31 - 22}{37-22})}{ln(8/9)}

t=\frac{ln(3/5)}{ln(8/9)}

t=\frac{ln(3/5)}{ln(8/9)}

t ≈ 4.337 hours from the time the body was killed to when the police found it.

The police found the body at 11:00PM so subtract 4.337 from that.

11 - 4.33 = 6.66 ≈ 6:30PM

You might be interested in
Explain the two advantages and the two disadvantages of fission as an energy source.
yawa3891 [41]

Answer with Explanation:

1) The advantages of fission energy are:

a) Higher concentration of energy : Concentration of energy or the energy density is defined as the amount of energy that is produced by burning a unit mass of the fuel. The nuclear energy obtained by fission has the highest energy density among all the other natural sources of energy such as coal,gas,e.t.c.

b) Cheap source of energy : The cost at which the energy is produced by a nuclear reactor after it is operational is the lowest among all the other sources of energy such as coal, solar,e.t.c

2) The disadvantages of fission energy are:

a) Highly dangerous residue: The fuel that is left unspent is highly radioactive and thus is very dangerous. Usually the residual material is taken deep into the earth for it's disposal.

b) It has high initial costs of design and development: The cost to design a nuclear reactor and to built one after it is designed is the most among all other types of energy sources and requires highly skilled personnel for operation.

6 0
2 years ago
You are a planning aide on a team and are given the assignment of researching the historical significance and original blueprint
LenKa [72]
I’m guessing it will be the second one!
8 0
2 years ago
It is known that the connecting rod AB exerts on the crank BCa 2.5-kN force directed down andto the left along the centerline of
monitta

Answer:

M_c = 61.6 Nm

Explanation:

Given:

F_a = 2.5 KN

Find:

Determine the moment of this force about C for the two casesshown.

Solution:

- Draw horizontal and vertical vectors at point A.

- Take moments about point C as follows:

                         M_c = F_a*( 42 / 150 ) *88

                         M_c = 2.5*( 42 / 150 ) *88

                         M_c = 61.6 Nm

- We see that the vertical component of force at point A passes through C.

Hence, its moment about C is zero.

6 0
3 years ago
Impact strips may be designed into a bumper cover.<br> True<br> False
d1i1m1o1n [39]

Answer:

true I think

Explanation:

true I think

5 0
3 years ago
Proper ventilation is required when welding, so that you don't ____________.
galben [10]
I say the answers is A but if you mean ventilation in the area of the room then answer B
4 0
3 years ago
Read 2 more answers
Other questions:
  • A turbine produces shaft power from a gas that enters the turbine with a (static) temperature of 628 K, a velocity of 143 m/s an
    7·1 answer
  • What is an ip<br> Number
    12·1 answer
  • Assume that we have a BS with a 6-dB antenna gain and an MS with antenna gain of 2 dB, at heights 10 m and 1.5 m, respectively,
    5·1 answer
  • How do I cancel my subscription
    12·2 answers
  • Show that -40 F is approximately equal to -40 C.
    12·1 answer
  • A specimen of some metal having a rectangular cross section 10.4 mm × 12.8 mm is pulled in tension with a force of 15900 N, whic
    6·1 answer
  • What are two reasons why Hunter edjucation is important?<br><br><br> 30 pts
    12·1 answer
  • Technician A says when you push the horn button, electromagnetism moves an iron bar inside the horn, which opens and closes cont
    5·2 answers
  • Which of the following can not be used to store an electrical charge?
    11·1 answer
  • a coiled spring is stretched 31.50 cm by a 2.00N weight. How far is it stretched by a 10.00 N weight?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!