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A brick wall of 20 cm thickness has thermal conductivity of 0.7 W/m K. An insulation of thermal conductivity 0.2 W/m K is to be applied on one side of the wall, so that the heat transfer through the wall is reduced by 75%. The same temperature difference is maintained across the wall before and after applying the insulation. Calculate the required thickness of insulation.?
Most Upvoted Answer
A brick wall of 20 cm thickness has thermal conductivity of 0.7 W/m K....
Given:
- Thickness of brick wall (x) = 20 cm = 0.2 m
- Thermal conductivity of brick wall (k1) = 0.7 W/m K
- Thermal conductivity of insulation (k2) = 0.2 W/m K
- Reduction in heat transfer through the wall (ΔQ) = 75%
To find:
- Required thickness of insulation (y)
Formula:
The rate of heat transfer (Q) is given by the formula:
Q = (k * A * ΔT) / d
Where:
- Q is the rate of heat transfer (W)
- k is the thermal conductivity (W/m K)
- A is the cross-sectional area perpendicular to the direction of heat transfer (m^2)
- ΔT is the temperature difference (K)
- d is the thickness of the material (m)
Calculation:
Let's assume the initial rate of heat transfer through the brick wall without insulation is Q1.
Step 1: Calculate the initial rate of heat transfer (Q1) through the brick wall without insulation.
Q1 = (k1 * A * ΔT) / x
Step 2: Calculate the final rate of heat transfer (Q2) through the wall with insulation.
Q2 = (k1 * A * ΔT) / (x + y)
Step 3: Calculate the reduction in heat transfer (ΔQ) using the given percentage.
ΔQ = Q1 - Q2
ΔQ = Q1 - (0.25 * Q1) [75% reduction]
ΔQ = 0.75 * Q1
Step 4: Substitute the values of Q1, Q2, and ΔQ into the equations and solve for y.
0.75 * Q1 = Q1 - (k1 * A * ΔT) / (x + y)
0.75 * (k1 * A * ΔT) / x = (k1 * A * ΔT) / (x + y)
0.75 * x = x + y
0.75 * x - x = y
0.25 * x = y
Therefore, the required thickness of insulation (y) is 0.25 times the thickness of the brick wall (x).
Final Answer:
The required thickness of insulation is 0.05 m (or 5 cm).
- Thickness of brick wall (x) = 20 cm = 0.2 m
- Thermal conductivity of brick wall (k1) = 0.7 W/m K
- Thermal conductivity of insulation (k2) = 0.2 W/m K
- Reduction in heat transfer through the wall (ΔQ) = 75%
To find:
- Required thickness of insulation (y)
Formula:
The rate of heat transfer (Q) is given by the formula:
Q = (k * A * ΔT) / d
Where:
- Q is the rate of heat transfer (W)
- k is the thermal conductivity (W/m K)
- A is the cross-sectional area perpendicular to the direction of heat transfer (m^2)
- ΔT is the temperature difference (K)
- d is the thickness of the material (m)
Calculation:
Let's assume the initial rate of heat transfer through the brick wall without insulation is Q1.
Step 1: Calculate the initial rate of heat transfer (Q1) through the brick wall without insulation.
Q1 = (k1 * A * ΔT) / x
Step 2: Calculate the final rate of heat transfer (Q2) through the wall with insulation.
Q2 = (k1 * A * ΔT) / (x + y)
Step 3: Calculate the reduction in heat transfer (ΔQ) using the given percentage.
ΔQ = Q1 - Q2
ΔQ = Q1 - (0.25 * Q1) [75% reduction]
ΔQ = 0.75 * Q1
Step 4: Substitute the values of Q1, Q2, and ΔQ into the equations and solve for y.
0.75 * Q1 = Q1 - (k1 * A * ΔT) / (x + y)
0.75 * (k1 * A * ΔT) / x = (k1 * A * ΔT) / (x + y)
0.75 * x = x + y
0.75 * x - x = y
0.25 * x = y
Therefore, the required thickness of insulation (y) is 0.25 times the thickness of the brick wall (x).
Final Answer:
The required thickness of insulation is 0.05 m (or 5 cm).
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A brick wall of 20 cm thickness has thermal conductivity of 0.7 W/m K. An insulation of thermal conductivity 0.2 W/m K is to be applied on one side of the wall, so that the heat transfer through the wall is reduced by 75%. The same temperature difference is maintained across the wall before and after applying the insulation. Calculate the required thickness of insulation.?
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A brick wall of 20 cm thickness has thermal conductivity of 0.7 W/m K. An insulation of thermal conductivity 0.2 W/m K is to be applied on one side of the wall, so that the heat transfer through the wall is reduced by 75%. The same temperature difference is maintained across the wall before and after applying the insulation. Calculate the required thickness of insulation.? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about A brick wall of 20 cm thickness has thermal conductivity of 0.7 W/m K. An insulation of thermal conductivity 0.2 W/m K is to be applied on one side of the wall, so that the heat transfer through the wall is reduced by 75%. The same temperature difference is maintained across the wall before and after applying the insulation. Calculate the required thickness of insulation.? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A brick wall of 20 cm thickness has thermal conductivity of 0.7 W/m K. An insulation of thermal conductivity 0.2 W/m K is to be applied on one side of the wall, so that the heat transfer through the wall is reduced by 75%. The same temperature difference is maintained across the wall before and after applying the insulation. Calculate the required thickness of insulation.?.
A brick wall of 20 cm thickness has thermal conductivity of 0.7 W/m K. An insulation of thermal conductivity 0.2 W/m K is to be applied on one side of the wall, so that the heat transfer through the wall is reduced by 75%. The same temperature difference is maintained across the wall before and after applying the insulation. Calculate the required thickness of insulation.? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about A brick wall of 20 cm thickness has thermal conductivity of 0.7 W/m K. An insulation of thermal conductivity 0.2 W/m K is to be applied on one side of the wall, so that the heat transfer through the wall is reduced by 75%. The same temperature difference is maintained across the wall before and after applying the insulation. Calculate the required thickness of insulation.? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A brick wall of 20 cm thickness has thermal conductivity of 0.7 W/m K. An insulation of thermal conductivity 0.2 W/m K is to be applied on one side of the wall, so that the heat transfer through the wall is reduced by 75%. The same temperature difference is maintained across the wall before and after applying the insulation. Calculate the required thickness of insulation.?.
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A brick wall of 20 cm thickness has thermal conductivity of 0.7 W/m K. An insulation of thermal conductivity 0.2 W/m K is to be applied on one side of the wall, so that the heat transfer through the wall is reduced by 75%. The same temperature difference is maintained across the wall before and after applying the insulation. Calculate the required thickness of insulation.?, a detailed solution for A brick wall of 20 cm thickness has thermal conductivity of 0.7 W/m K. An insulation of thermal conductivity 0.2 W/m K is to be applied on one side of the wall, so that the heat transfer through the wall is reduced by 75%. The same temperature difference is maintained across the wall before and after applying the insulation. Calculate the required thickness of insulation.? has been provided alongside types of A brick wall of 20 cm thickness has thermal conductivity of 0.7 W/m K. An insulation of thermal conductivity 0.2 W/m K is to be applied on one side of the wall, so that the heat transfer through the wall is reduced by 75%. The same temperature difference is maintained across the wall before and after applying the insulation. Calculate the required thickness of insulation.? theory, EduRev gives you an
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