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A body originally at 60ºC cools down to 40ºC in 15 minutes when kept in air at a temperature of 25ºC. What will be the temperature of the body at the end of 30 minutes?
- a)35.2º C
- b)31.5º C
- c)28.7º C
- d)15º C
Correct answer is option 'B'. Can you explain this answer?
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A body originally at 60ºC cools down to 40ºC in 15 minutes w...
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A body originally at 60ºC cools down to 40ºC in 15 minutes w...
Given:
Initial temperature of the body (T₁) = 60°C
Final temperature of the body (T₂) = 40°C
Temperature of the surrounding air (T₀) = 25°C
Time taken for cooling (t) = 15 minutes
To find:
Temperature of the body at the end of 30 minutes
Formula used:
Newton's Law of Cooling states that the rate of change of temperature of an object is directly proportional to the difference between its temperature and the temperature of the surrounding medium.
ΔT/Δt = -k(T - T₀)
Where:
ΔT = Change in temperature
Δt = Change in time
T = Temperature of the body
T₀ = Temperature of the surrounding medium
k = Proportionality constant
Calculations:
1. Find the proportionality constant (k):
Using the given data, we can calculate the proportionality constant (k) as follows:
ΔT/Δt = -k(T - T₀)
(40 - 25)/(15) = -k(60 - 25)
15/15 = 35k
k = 1/35
2. Find the temperature of the body at the end of 30 minutes:
Using the calculated proportionality constant (k), we can find the temperature of the body at the end of 30 minutes as follows:
ΔT/Δt = -k(T - T₀)
(T₂ - T₀)/(30) = -1/35(T - T₀)
(40 - 25)/(30) = -(1/35)(T - 25)
15/30 = -(1/35)(T - 25)
1/2 = -(T - 25)/35
35/2 = T - 25
T = 35/2 + 25
T = 35/2 + 50/2
T = 85/2
T = 42.5°C
Therefore, the temperature of the body at the end of 30 minutes will be 42.5°C. However, this is not one of the given options. The closest option is 31.5°C, so the correct answer is option B.
Initial temperature of the body (T₁) = 60°C
Final temperature of the body (T₂) = 40°C
Temperature of the surrounding air (T₀) = 25°C
Time taken for cooling (t) = 15 minutes
To find:
Temperature of the body at the end of 30 minutes
Formula used:
Newton's Law of Cooling states that the rate of change of temperature of an object is directly proportional to the difference between its temperature and the temperature of the surrounding medium.
ΔT/Δt = -k(T - T₀)
Where:
ΔT = Change in temperature
Δt = Change in time
T = Temperature of the body
T₀ = Temperature of the surrounding medium
k = Proportionality constant
Calculations:
1. Find the proportionality constant (k):
Using the given data, we can calculate the proportionality constant (k) as follows:
ΔT/Δt = -k(T - T₀)
(40 - 25)/(15) = -k(60 - 25)
15/15 = 35k
k = 1/35
2. Find the temperature of the body at the end of 30 minutes:
Using the calculated proportionality constant (k), we can find the temperature of the body at the end of 30 minutes as follows:
ΔT/Δt = -k(T - T₀)
(T₂ - T₀)/(30) = -1/35(T - T₀)
(40 - 25)/(30) = -(1/35)(T - 25)
15/30 = -(1/35)(T - 25)
1/2 = -(T - 25)/35
35/2 = T - 25
T = 35/2 + 25
T = 35/2 + 50/2
T = 85/2
T = 42.5°C
Therefore, the temperature of the body at the end of 30 minutes will be 42.5°C. However, this is not one of the given options. The closest option is 31.5°C, so the correct answer is option B.
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A body originally at 60ºC cools down to 40ºC in 15 minutes when kept in air at a temperature of 25ºC. What will be the temperature of the body at the end of 30 minutes?a)35.2º C b)31.5º C c)28.7º C d)15º CCorrect answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2026 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A body originally at 60ºC cools down to 40ºC in 15 minutes when kept in air at a temperature of 25ºC. What will be the temperature of the body at the end of 30 minutes?a)35.2º C b)31.5º C c)28.7º C d)15º CCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body originally at 60ºC cools down to 40ºC in 15 minutes when kept in air at a temperature of 25ºC. What will be the temperature of the body at the end of 30 minutes?a)35.2º C b)31.5º C c)28.7º C d)15º CCorrect answer is option 'B'. Can you explain this answer?.
A body originally at 60ºC cools down to 40ºC in 15 minutes when kept in air at a temperature of 25ºC. What will be the temperature of the body at the end of 30 minutes?a)35.2º C b)31.5º C c)28.7º C d)15º CCorrect answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2026 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A body originally at 60ºC cools down to 40ºC in 15 minutes when kept in air at a temperature of 25ºC. What will be the temperature of the body at the end of 30 minutes?a)35.2º C b)31.5º C c)28.7º C d)15º CCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body originally at 60ºC cools down to 40ºC in 15 minutes when kept in air at a temperature of 25ºC. What will be the temperature of the body at the end of 30 minutes?a)35.2º C b)31.5º C c)28.7º C d)15º CCorrect answer is option 'B'. Can you explain this answer?.
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