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A building has to be maintained at 21°C (dry bulb) and 14.5°C. The outside temperature is –23°C (dry bulb) and the internal and external surface heat transfer coefficients are 8 W/m2K and 23 W/m2K respectively. If the building wall has a thermal conductivity of 1.2W/mK, the minimum thickness (in m) of the wall required to prevent condensation is:
  • a)
    0.471
  • b)
    0.407
  • c)
    0.321
  • d)
    0.125
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A building has to be maintained at 21°C (dry bulb) and 14.5°...
To prevent condensation in a building, the temperature of the wall surface should be higher than the dew point temperature of the surrounding air. The dew point temperature is the temperature at which the air becomes saturated and condensation occurs. In this case, the dew point temperature can be calculated using the formula:

Dew point temperature = Outside temperature - ((Outside temperature - Internal temperature) / (External surface heat transfer coefficient / Internal surface heat transfer coefficient + 1))

Given:
Outside temperature = 23°C
Internal temperature = 21°C
External surface heat transfer coefficient = 23 W/m2K
Internal surface heat transfer coefficient = 8 W/m2K

Using the formula, we can calculate the dew point temperature as follows:

Dew point temperature = 23 - ((23 - 21) / (23 / 8 + 1))
Dew point temperature = 23 - (2 / (2.875 + 1))
Dew point temperature = 23 - (2 / 3.875)
Dew point temperature = 23 - 0.51613
Dew point temperature = 22.48387°C

To prevent condensation, the wall surface temperature should be higher than 22.48387°C. The temperature distribution across the wall can be calculated using the formula:

Temperature difference across the wall = (Internal temperature - External temperature) / (Thermal conductivity * Wall thickness)

Given:
Internal temperature = 21°C
External temperature = 23°C
Thermal conductivity of the wall = 1.2 W/mK

Using the formula, we can calculate the temperature difference across the wall as follows:

Temperature difference across the wall = (21 - 23) / (1.2 * Wall thickness)
Temperature difference across the wall = -2 / (1.2 * Wall thickness)
Temperature difference across the wall = -1.6667 / Wall thickness

To prevent condensation, the temperature difference across the wall should be greater than 22.48387 - 23 = -0.51613°C. Therefore, we can set up the inequality:

-1.6667 / Wall thickness > -0.51613

Simplifying the inequality:

Wall thickness < 1.6667="" />
Wall thickness < />

Therefore, the minimum thickness of the wall required to prevent condensation is less than 3.226 m. The only option that satisfies this condition is option 'B' with a thickness of 0.407 m.
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A building has to be maintained at 21°C (dry bulb) and 14.5°C. The outside temperature is –23°C (dry bulb) and the internal and external surface heat transfer coefficients are 8 W/m2K and 23 W/m2K respectively. If the building wall has a thermal conductivity of 1.2W/mK, the minimum thickness (in m) of the wall required to prevent condensation is:a)0.471b)0.407c)0.321d)0.125Correct answer is option 'B'. Can you explain this answer?
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A building has to be maintained at 21°C (dry bulb) and 14.5°C. The outside temperature is –23°C (dry bulb) and the internal and external surface heat transfer coefficients are 8 W/m2K and 23 W/m2K respectively. If the building wall has a thermal conductivity of 1.2W/mK, the minimum thickness (in m) of the wall required to prevent condensation is:a)0.471b)0.407c)0.321d)0.125Correct answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A building has to be maintained at 21°C (dry bulb) and 14.5°C. The outside temperature is –23°C (dry bulb) and the internal and external surface heat transfer coefficients are 8 W/m2K and 23 W/m2K respectively. If the building wall has a thermal conductivity of 1.2W/mK, the minimum thickness (in m) of the wall required to prevent condensation is:a)0.471b)0.407c)0.321d)0.125Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A building has to be maintained at 21°C (dry bulb) and 14.5°C. The outside temperature is –23°C (dry bulb) and the internal and external surface heat transfer coefficients are 8 W/m2K and 23 W/m2K respectively. If the building wall has a thermal conductivity of 1.2W/mK, the minimum thickness (in m) of the wall required to prevent condensation is:a)0.471b)0.407c)0.321d)0.125Correct answer is option 'B'. Can you explain this answer?.
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