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Heat is conducted through a uniform tapered rod of cross section and length 50 cm. At the left end side of face is 3 cm and temperature 600c. At the right end the corresponding value are 8 cm and 150'c determine 1- The rate of heat conduction 2- The temperature at the point 30 cm from hot end Themal conductivity of rod 60 w/Mc and heat is conducted only along length of rod?
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Heat is conducted through a uniform tapered rod of cross section and l...
1. Rate of Heat Conduction:
To determine the rate of heat conduction, we need to use Fourier's Law of Heat Conduction, which states that the rate of heat conduction through a material is proportional to the temperature gradient across the material.
The formula for heat conduction is given by:
Q = k * A * (ΔT / L)
Where:
Q is the rate of heat conduction,
k is the thermal conductivity of the material,
A is the cross-sectional area of the rod,
ΔT is the temperature difference across the rod,
L is the length of the rod.
Given:
Length of the rod (L) = 50 cm
Temperature at the left end (T1) = 60 °C
Temperature at the right end (T2) = 150 °C
Cross-sectional area at the left end (A1) = 3 cm^2
Cross-sectional area at the right end (A2) = 8 cm^2
Thermal conductivity of the rod (k) = 60 W/m°C
Cross-sectional area at the point 30 cm from the hot end (A) can be calculated using similar triangles:
A = A1 + (A2 - A1) * (30 cm / 50 cm)
A = 3 cm^2 + (8 cm^2 - 3 cm^2) * (30 cm / 50 cm)
A = 4.6 cm^2
Temperature difference across the rod (ΔT) is given by:
ΔT = T2 - T1
ΔT = 150 °C - 60 °C
ΔT = 90 °C
Substituting the values into the formula, we get:
Q = 60 W/m°C * 0.046 m^2 * (90 °C / 0.5 m)
Q = 552 W
Therefore, the rate of heat conduction through the rod is 552 W.
2. Temperature at the Point 30 cm from the Hot End:
To determine the temperature at a specific point along the rod, we can use the equation for heat conduction and rearrange it to solve for ΔT.
The formula for temperature difference (ΔT) is given by:
ΔT = Q * L / (k * A)
Given:
Rate of heat conduction (Q) = 552 W
Length of the rod (L) = 50 cm
Thermal conductivity of the rod (k) = 60 W/m°C
Cross-sectional area at the point 30 cm from the hot end (A) = 4.6 cm^2
Substituting the values into the formula, we get:
ΔT = 552 W * 0.5 m / (60 W/m°C * 0.046 m^2)
ΔT = 95 °C
Since the temperature at the hot end (T1) is 60 °C, we can calculate the temperature at the point 30 cm from the hot end (T) as follows:
T = T1 + ΔT
T = 60 °C + 95 °C
T = 155 °C
Therefore, the temperature at the point 30 cm from the hot end is 155 °C.
To determine the rate of heat conduction, we need to use Fourier's Law of Heat Conduction, which states that the rate of heat conduction through a material is proportional to the temperature gradient across the material.
The formula for heat conduction is given by:
Q = k * A * (ΔT / L)
Where:
Q is the rate of heat conduction,
k is the thermal conductivity of the material,
A is the cross-sectional area of the rod,
ΔT is the temperature difference across the rod,
L is the length of the rod.
Given:
Length of the rod (L) = 50 cm
Temperature at the left end (T1) = 60 °C
Temperature at the right end (T2) = 150 °C
Cross-sectional area at the left end (A1) = 3 cm^2
Cross-sectional area at the right end (A2) = 8 cm^2
Thermal conductivity of the rod (k) = 60 W/m°C
Cross-sectional area at the point 30 cm from the hot end (A) can be calculated using similar triangles:
A = A1 + (A2 - A1) * (30 cm / 50 cm)
A = 3 cm^2 + (8 cm^2 - 3 cm^2) * (30 cm / 50 cm)
A = 4.6 cm^2
Temperature difference across the rod (ΔT) is given by:
ΔT = T2 - T1
ΔT = 150 °C - 60 °C
ΔT = 90 °C
Substituting the values into the formula, we get:
Q = 60 W/m°C * 0.046 m^2 * (90 °C / 0.5 m)
Q = 552 W
Therefore, the rate of heat conduction through the rod is 552 W.
2. Temperature at the Point 30 cm from the Hot End:
To determine the temperature at a specific point along the rod, we can use the equation for heat conduction and rearrange it to solve for ΔT.
The formula for temperature difference (ΔT) is given by:
ΔT = Q * L / (k * A)
Given:
Rate of heat conduction (Q) = 552 W
Length of the rod (L) = 50 cm
Thermal conductivity of the rod (k) = 60 W/m°C
Cross-sectional area at the point 30 cm from the hot end (A) = 4.6 cm^2
Substituting the values into the formula, we get:
ΔT = 552 W * 0.5 m / (60 W/m°C * 0.046 m^2)
ΔT = 95 °C
Since the temperature at the hot end (T1) is 60 °C, we can calculate the temperature at the point 30 cm from the hot end (T) as follows:
T = T1 + ΔT
T = 60 °C + 95 °C
T = 155 °C
Therefore, the temperature at the point 30 cm from the hot end is 155 °C.
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Heat is conducted through a uniform tapered rod of cross section and length 50 cm. At the left end side of face is 3 cm and temperature 600c. At the right end the corresponding value are 8 cm and 150'c determine 1- The rate of heat conduction 2- The temperature at the point 30 cm from hot end Themal conductivity of rod 60 w/Mc and heat is conducted only along length of rod?
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Heat is conducted through a uniform tapered rod of cross section and length 50 cm. At the left end side of face is 3 cm and temperature 600c. At the right end the corresponding value are 8 cm and 150'c determine 1- The rate of heat conduction 2- The temperature at the point 30 cm from hot end Themal conductivity of rod 60 w/Mc and heat is conducted only along length of rod? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Heat is conducted through a uniform tapered rod of cross section and length 50 cm. At the left end side of face is 3 cm and temperature 600c. At the right end the corresponding value are 8 cm and 150'c determine 1- The rate of heat conduction 2- The temperature at the point 30 cm from hot end Themal conductivity of rod 60 w/Mc and heat is conducted only along length of rod? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Heat is conducted through a uniform tapered rod of cross section and length 50 cm. At the left end side of face is 3 cm and temperature 600c. At the right end the corresponding value are 8 cm and 150'c determine 1- The rate of heat conduction 2- The temperature at the point 30 cm from hot end Themal conductivity of rod 60 w/Mc and heat is conducted only along length of rod?.
Heat is conducted through a uniform tapered rod of cross section and length 50 cm. At the left end side of face is 3 cm and temperature 600c. At the right end the corresponding value are 8 cm and 150'c determine 1- The rate of heat conduction 2- The temperature at the point 30 cm from hot end Themal conductivity of rod 60 w/Mc and heat is conducted only along length of rod? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Heat is conducted through a uniform tapered rod of cross section and length 50 cm. At the left end side of face is 3 cm and temperature 600c. At the right end the corresponding value are 8 cm and 150'c determine 1- The rate of heat conduction 2- The temperature at the point 30 cm from hot end Themal conductivity of rod 60 w/Mc and heat is conducted only along length of rod? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Heat is conducted through a uniform tapered rod of cross section and length 50 cm. At the left end side of face is 3 cm and temperature 600c. At the right end the corresponding value are 8 cm and 150'c determine 1- The rate of heat conduction 2- The temperature at the point 30 cm from hot end Themal conductivity of rod 60 w/Mc and heat is conducted only along length of rod?.
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