GATE Exam > GATE Questions > A person is found dead at 5 pm in a room who...
Start Learning for Free
A person is found dead at 5 pm in a room whose temperature is 20 degrees Celsius. The body temperature is measured to be 25 degrees Celsius when found. The heat transfer coefficient is estimated to be 8 W/m2 K. Modeling the body as a 30 cm diameter, 1.7 cm long cylinder. Estimate the time of death of the person.
- a)13.55 seconds
- b)12.55 seconds
- c)11.55 seconds
- d)10.55 seconds
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A person is found dead at 5 pm in a room whose temperature is 20 degr...
Tt – T INFINITY / T i – T INFINITY = e – b T.
View all questions of this test
Most Upvoted Answer
A person is found dead at 5 pm in a room whose temperature is 20 degr...
Given data:
Temperature of the room = 20°C
Temperature of the body when found = 25°C
Heat transfer coefficient = 8 W/m²K
Diameter of the body = 30 cm
Length of the body = 1.7 cm
To find: Time of death of the person
Solution:
1. Calculate the surface area of the body:
The surface area of the cylinder can be calculated as:
Surface area = 2πrL + 2πr²
where r = radius of the cylinder = diameter / 2 = 15 cm
L = length of the cylinder = 1.7 cm
Substituting the values, we get:
Surface area = 2π(15 cm)(1.7 cm) + 2π(15 cm)²
Surface area = 319.98 cm²
2. Calculate the heat loss from the body:
The heat loss from the body can be calculated using Newton's law of cooling, which states that:
Rate of heat loss = hA(Tbody - Troom)
where h = heat transfer coefficient = 8 W/m²K
A = surface area of the body in m²
Tbody = temperature of the body when found = 25°C
Troom = temperature of the room = 20°C
Converting units, we get:
h = 8 W/m²K = 0.008 W/cm²K
A = 319.98 cm² = 0.031998 m²
Tbody = 25°C = 298 K
Troom = 20°C = 293 K
Substituting the values, we get:
Rate of heat loss = 0.008 W/cm²K × 0.031998 m² × (298 K - 293 K)
Rate of heat loss = 0.004031 W
3. Calculate the initial temperature of the body:
The initial temperature of the body can be calculated using the formula:
Tbody = Troom + (Tinitial - Troom)e^(-ht/mc)
where Tinitial = initial temperature of the body
t = time elapsed since death
m = mass of the body
c = specific heat capacity of the body
Assuming the mass of the body to be 70 kg (average for an adult), and the specific heat capacity of the body to be 3.5 J/gK, we get:
m = 70 kg × 1000 g/kg = 70000 g
c = 3.5 J/gK
Substituting the values, we get:
25°C = 20°C + (Tinitial - 20°C)e^(-0.008t/70000×3.5)
5 = (Tinitial - 20°C)e^(-0.0000008t)
ln(5) = ln(Tinitial - 20°C) - 0.0000008t
ln(Tinitial - 20°C) = ln(5) + 0.0000008t
Tinitial - 20°C = e^(ln(5) + 0.0000008t)
Tinitial = e^(ln(5) + 0.0000008t) + 20°C
4. Calculate the time of death:
Substituting the initial temperature of the body as 37°C (average human body temperature),
Temperature of the room = 20°C
Temperature of the body when found = 25°C
Heat transfer coefficient = 8 W/m²K
Diameter of the body = 30 cm
Length of the body = 1.7 cm
To find: Time of death of the person
Solution:
1. Calculate the surface area of the body:
The surface area of the cylinder can be calculated as:
Surface area = 2πrL + 2πr²
where r = radius of the cylinder = diameter / 2 = 15 cm
L = length of the cylinder = 1.7 cm
Substituting the values, we get:
Surface area = 2π(15 cm)(1.7 cm) + 2π(15 cm)²
Surface area = 319.98 cm²
2. Calculate the heat loss from the body:
The heat loss from the body can be calculated using Newton's law of cooling, which states that:
Rate of heat loss = hA(Tbody - Troom)
where h = heat transfer coefficient = 8 W/m²K
A = surface area of the body in m²
Tbody = temperature of the body when found = 25°C
Troom = temperature of the room = 20°C
Converting units, we get:
h = 8 W/m²K = 0.008 W/cm²K
A = 319.98 cm² = 0.031998 m²
Tbody = 25°C = 298 K
Troom = 20°C = 293 K
Substituting the values, we get:
Rate of heat loss = 0.008 W/cm²K × 0.031998 m² × (298 K - 293 K)
Rate of heat loss = 0.004031 W
3. Calculate the initial temperature of the body:
The initial temperature of the body can be calculated using the formula:
Tbody = Troom + (Tinitial - Troom)e^(-ht/mc)
where Tinitial = initial temperature of the body
t = time elapsed since death
m = mass of the body
c = specific heat capacity of the body
Assuming the mass of the body to be 70 kg (average for an adult), and the specific heat capacity of the body to be 3.5 J/gK, we get:
m = 70 kg × 1000 g/kg = 70000 g
c = 3.5 J/gK
Substituting the values, we get:
25°C = 20°C + (Tinitial - 20°C)e^(-0.008t/70000×3.5)
5 = (Tinitial - 20°C)e^(-0.0000008t)
ln(5) = ln(Tinitial - 20°C) - 0.0000008t
ln(Tinitial - 20°C) = ln(5) + 0.0000008t
Tinitial - 20°C = e^(ln(5) + 0.0000008t)
Tinitial = e^(ln(5) + 0.0000008t) + 20°C
4. Calculate the time of death:
Substituting the initial temperature of the body as 37°C (average human body temperature),
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
A person is found dead at 5 pm in a room whose temperature is 20 degrees Celsius. The body temperature is measured to be 25 degrees Celsius when found. The heat transfer coefficient is estimated to be 8 W/m2 K. Modeling the body as a 30 cm diameter, 1.7 cm long cylinder. Estimate the time of death of the person.a)13.55 secondsb)12.55 secondsc)11.55 secondsd)10.55 secondsCorrect answer is option 'D'. Can you explain this answer?
Question Description
A person is found dead at 5 pm in a room whose temperature is 20 degrees Celsius. The body temperature is measured to be 25 degrees Celsius when found. The heat transfer coefficient is estimated to be 8 W/m2 K. Modeling the body as a 30 cm diameter, 1.7 cm long cylinder. Estimate the time of death of the person.a)13.55 secondsb)12.55 secondsc)11.55 secondsd)10.55 secondsCorrect answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A person is found dead at 5 pm in a room whose temperature is 20 degrees Celsius. The body temperature is measured to be 25 degrees Celsius when found. The heat transfer coefficient is estimated to be 8 W/m2 K. Modeling the body as a 30 cm diameter, 1.7 cm long cylinder. Estimate the time of death of the person.a)13.55 secondsb)12.55 secondsc)11.55 secondsd)10.55 secondsCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person is found dead at 5 pm in a room whose temperature is 20 degrees Celsius. The body temperature is measured to be 25 degrees Celsius when found. The heat transfer coefficient is estimated to be 8 W/m2 K. Modeling the body as a 30 cm diameter, 1.7 cm long cylinder. Estimate the time of death of the person.a)13.55 secondsb)12.55 secondsc)11.55 secondsd)10.55 secondsCorrect answer is option 'D'. Can you explain this answer?.
A person is found dead at 5 pm in a room whose temperature is 20 degrees Celsius. The body temperature is measured to be 25 degrees Celsius when found. The heat transfer coefficient is estimated to be 8 W/m2 K. Modeling the body as a 30 cm diameter, 1.7 cm long cylinder. Estimate the time of death of the person.a)13.55 secondsb)12.55 secondsc)11.55 secondsd)10.55 secondsCorrect answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A person is found dead at 5 pm in a room whose temperature is 20 degrees Celsius. The body temperature is measured to be 25 degrees Celsius when found. The heat transfer coefficient is estimated to be 8 W/m2 K. Modeling the body as a 30 cm diameter, 1.7 cm long cylinder. Estimate the time of death of the person.a)13.55 secondsb)12.55 secondsc)11.55 secondsd)10.55 secondsCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person is found dead at 5 pm in a room whose temperature is 20 degrees Celsius. The body temperature is measured to be 25 degrees Celsius when found. The heat transfer coefficient is estimated to be 8 W/m2 K. Modeling the body as a 30 cm diameter, 1.7 cm long cylinder. Estimate the time of death of the person.a)13.55 secondsb)12.55 secondsc)11.55 secondsd)10.55 secondsCorrect answer is option 'D'. Can you explain this answer?.
Solutions for A person is found dead at 5 pm in a room whose temperature is 20 degrees Celsius. The body temperature is measured to be 25 degrees Celsius when found. The heat transfer coefficient is estimated to be 8 W/m2 K. Modeling the body as a 30 cm diameter, 1.7 cm long cylinder. Estimate the time of death of the person.a)13.55 secondsb)12.55 secondsc)11.55 secondsd)10.55 secondsCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of A person is found dead at 5 pm in a room whose temperature is 20 degrees Celsius. The body temperature is measured to be 25 degrees Celsius when found. The heat transfer coefficient is estimated to be 8 W/m2 K. Modeling the body as a 30 cm diameter, 1.7 cm long cylinder. Estimate the time of death of the person.a)13.55 secondsb)12.55 secondsc)11.55 secondsd)10.55 secondsCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A person is found dead at 5 pm in a room whose temperature is 20 degrees Celsius. The body temperature is measured to be 25 degrees Celsius when found. The heat transfer coefficient is estimated to be 8 W/m2 K. Modeling the body as a 30 cm diameter, 1.7 cm long cylinder. Estimate the time of death of the person.a)13.55 secondsb)12.55 secondsc)11.55 secondsd)10.55 secondsCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for A person is found dead at 5 pm in a room whose temperature is 20 degrees Celsius. The body temperature is measured to be 25 degrees Celsius when found. The heat transfer coefficient is estimated to be 8 W/m2 K. Modeling the body as a 30 cm diameter, 1.7 cm long cylinder. Estimate the time of death of the person.a)13.55 secondsb)12.55 secondsc)11.55 secondsd)10.55 secondsCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of A person is found dead at 5 pm in a room whose temperature is 20 degrees Celsius. The body temperature is measured to be 25 degrees Celsius when found. The heat transfer coefficient is estimated to be 8 W/m2 K. Modeling the body as a 30 cm diameter, 1.7 cm long cylinder. Estimate the time of death of the person.a)13.55 secondsb)12.55 secondsc)11.55 secondsd)10.55 secondsCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A person is found dead at 5 pm in a room whose temperature is 20 degrees Celsius. The body temperature is measured to be 25 degrees Celsius when found. The heat transfer coefficient is estimated to be 8 W/m2 K. Modeling the body as a 30 cm diameter, 1.7 cm long cylinder. Estimate the time of death of the person.a)13.55 secondsb)12.55 secondsc)11.55 secondsd)10.55 secondsCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup