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A composite wall of a furnace has 2 layers of equal thickness having thermal conductivities in the ratio of 3 : 2. What is the ratio of the temperature drop across the two layers?
- a)2:3
- b)3: 2
- c)1: 2
- d)loge2: loge3
Correct answer is option 'A'. Can you explain this answer?
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Ratio of Thermal Conductivities
The ratio of thermal conductivities of the two layers is given as 3:2. Let's assume the thermal conductivities of the two layers as k1 and k2, where k1 is the thermal conductivity of the first layer and k2 is the thermal conductivity of the second layer.
Given: k1:k2 = 3:2
Ratio of Temperature Drop
To find the ratio of the temperature drop across the two layers, we need to consider the equation for heat transfer through a composite wall.
According to Fourier's law of heat conduction, the rate of heat transfer through a material is directly proportional to the temperature difference across the material and inversely proportional to its thickness and thermal conductivity.
Mathematically, this can be expressed as:
Q = (kAΔT)/d
Where:
Q is the heat transfer rate,
k is the thermal conductivity,
A is the cross-sectional area of the material,
ΔT is the temperature difference across the material, and
d is the thickness of the material.
Since the thickness of the two layers is equal, we can assume that the cross-sectional area and thickness are the same for both layers.
Applying this equation to both layers, we have:
Q1 = (k1AΔT1)/d ---(1)
Q2 = (k2AΔT2)/d ---(2)
Since the cross-sectional area, thickness, and temperature difference are the same for both layers, we can cancel out these terms and rewrite the equations as:
Q1 = k1 ---(3)
Q2 = k2 ---(4)
Ratio of Temperature Drop across Layers
The heat transfer rate through a material is directly proportional to the thermal conductivity of that material. Therefore, the ratio of the heat transfer rates (Q1:Q2) is equal to the ratio of the thermal conductivities (k1:k2).
Q1:Q2 = k1:k2 = 3:2
Since the heat transfer rate is directly proportional to the temperature difference, we can conclude that the ratio of the temperature drops across the two layers is also 3:2.
Therefore, the correct answer is option 'A': 2:3
The ratio of thermal conductivities of the two layers is given as 3:2. Let's assume the thermal conductivities of the two layers as k1 and k2, where k1 is the thermal conductivity of the first layer and k2 is the thermal conductivity of the second layer.
Given: k1:k2 = 3:2
Ratio of Temperature Drop
To find the ratio of the temperature drop across the two layers, we need to consider the equation for heat transfer through a composite wall.
According to Fourier's law of heat conduction, the rate of heat transfer through a material is directly proportional to the temperature difference across the material and inversely proportional to its thickness and thermal conductivity.
Mathematically, this can be expressed as:
Q = (kAΔT)/d
Where:
Q is the heat transfer rate,
k is the thermal conductivity,
A is the cross-sectional area of the material,
ΔT is the temperature difference across the material, and
d is the thickness of the material.
Since the thickness of the two layers is equal, we can assume that the cross-sectional area and thickness are the same for both layers.
Applying this equation to both layers, we have:
Q1 = (k1AΔT1)/d ---(1)
Q2 = (k2AΔT2)/d ---(2)
Since the cross-sectional area, thickness, and temperature difference are the same for both layers, we can cancel out these terms and rewrite the equations as:
Q1 = k1 ---(3)
Q2 = k2 ---(4)
Ratio of Temperature Drop across Layers
The heat transfer rate through a material is directly proportional to the thermal conductivity of that material. Therefore, the ratio of the heat transfer rates (Q1:Q2) is equal to the ratio of the thermal conductivities (k1:k2).
Q1:Q2 = k1:k2 = 3:2
Since the heat transfer rate is directly proportional to the temperature difference, we can conclude that the ratio of the temperature drops across the two layers is also 3:2.
Therefore, the correct answer is option 'A': 2:3
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A composite wall of a furnace has 2 layers of equal thickness having thermal conductivities in the ratio of 3 : 2. What is the ratio of the temperature drop across the two layers?a)2:3b)3: 2c)1: 2d)loge2: loge3Correct answer is option 'A'. Can you explain this answer?
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