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A tapered stainless steel rod, perfectly insulated on the curved surface, has end diameters of 6 cm and 12 cm respectively, and is 20 cm long. The thicker end is fixed to a hot wall and the thinner end is maintained at 25°C. The steady state rate of heat loss through the rod is estimated to be 50W. Calculate the temperature at the hot end of the rod. Take thermal conductivity of the rod material as 15 W/m-°C
- a)142
- b)143
Correct answer is between '142,143'. Can you explain this answer?
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A tapered stainless steel rod, perfectly insulated on the curved surf...
The perfectly insulated curved surface implies that the situation corresponds to one-dimensional conduction in the x-direction only for which
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Where Ax is the cross-sectional area at any axial position x from the thinner end of the rod.
Radius at distance x:
Then
Separating the variables and upon integration,
we get
Putting the value of 
in the above expression,
in the above expression,Refer figure
r1 = 3 cm;r2 = 6 cm;t1 = 25°C
The heat flow is from thicker to thinner end
and so Q = -50 W
Substituting the given data in the expression
derived above,
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A tapered stainless steel rod, perfectly insulated on the curved surf...
Given:
- End diameters of the rod: 6 cm and 12 cm
- Length of the rod: 20 cm
- Rate of heat loss through the rod: 50 W
- Thermal conductivity of the rod material: 15 W/m-°C
To Find:
Temperature at the hot end of the rod
Assumptions:
- Steady-state conditions are assumed.
- The rod is perfectly insulated on the curved surface, meaning that heat transfer occurs only through conduction along the length of the rod.
- The rod is assumed to be homogeneous and isotropic.
Approach:
1. Calculate the cross-sectional areas of the rod at both ends.
2. Use the formula for heat conduction through a cylindrical rod to calculate the rate of heat transfer through the rod.
3. Set up an equation using the calculated rate of heat loss and solve for the temperature at the hot end of the rod.
Solution:
Step 1: Calculate the cross-sectional areas of the rod at both ends.
- Area of the larger end: A1 = πr1² = π(12/2)² = 36π cm²
- Area of the smaller end: A2 = πr2² = π(6/2)² = 9π cm²
Step 2: Calculate the rate of heat transfer through the rod.
- The rate of heat transfer through a cylindrical rod is given by the formula:
Q = kAΔT/ L
where Q is the rate of heat transfer, k is the thermal conductivity of the rod material, A is the cross-sectional area of the rod, ΔT is the temperature difference along the length of the rod, and L is the length of the rod.
- Rearranging the formula, we get:
ΔT = QL/(kA)
- Substituting the given values:
ΔT = 50 W * 0.2 m / (15 W/m-°C * (36π - 9π) cm²)
= 10 / (15 * 27π) °C
≈ 0.012 °C
Step 3: Calculate the temperature at the hot end of the rod.
- The temperature difference along the length of the rod can be calculated as:
ΔT = Th - Tc
where Th is the temperature at the hot end and Tc is the temperature at the cold end.
- Rearranging the formula, we get:
Th = ΔT + Tc
- Substituting the values:
Th = 0.012 °C + 25 °C
≈ 25.012 °C
Answer:
The temperature at the hot end of the rod is approximately 25.012 °C, which can be rounded to 25 °C.
- End diameters of the rod: 6 cm and 12 cm
- Length of the rod: 20 cm
- Rate of heat loss through the rod: 50 W
- Thermal conductivity of the rod material: 15 W/m-°C
To Find:
Temperature at the hot end of the rod
Assumptions:
- Steady-state conditions are assumed.
- The rod is perfectly insulated on the curved surface, meaning that heat transfer occurs only through conduction along the length of the rod.
- The rod is assumed to be homogeneous and isotropic.
Approach:
1. Calculate the cross-sectional areas of the rod at both ends.
2. Use the formula for heat conduction through a cylindrical rod to calculate the rate of heat transfer through the rod.
3. Set up an equation using the calculated rate of heat loss and solve for the temperature at the hot end of the rod.
Solution:
Step 1: Calculate the cross-sectional areas of the rod at both ends.
- Area of the larger end: A1 = πr1² = π(12/2)² = 36π cm²
- Area of the smaller end: A2 = πr2² = π(6/2)² = 9π cm²
Step 2: Calculate the rate of heat transfer through the rod.
- The rate of heat transfer through a cylindrical rod is given by the formula:
Q = kAΔT/ L
where Q is the rate of heat transfer, k is the thermal conductivity of the rod material, A is the cross-sectional area of the rod, ΔT is the temperature difference along the length of the rod, and L is the length of the rod.
- Rearranging the formula, we get:
ΔT = QL/(kA)
- Substituting the given values:
ΔT = 50 W * 0.2 m / (15 W/m-°C * (36π - 9π) cm²)
= 10 / (15 * 27π) °C
≈ 0.012 °C
Step 3: Calculate the temperature at the hot end of the rod.
- The temperature difference along the length of the rod can be calculated as:
ΔT = Th - Tc
where Th is the temperature at the hot end and Tc is the temperature at the cold end.
- Rearranging the formula, we get:
Th = ΔT + Tc
- Substituting the values:
Th = 0.012 °C + 25 °C
≈ 25.012 °C
Answer:
The temperature at the hot end of the rod is approximately 25.012 °C, which can be rounded to 25 °C.
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A tapered stainless steel rod, perfectly insulated on the curved surface, has end diameters of 6 cm and 12 cm respectively, and is 20 cm long. The thicker end is fixed to a hot wall and the thinner end is maintained at 25°C. The steady state rate of heat loss through the rod is estimated to be 50W. Calculate the temperature at the hot end of the rod. Take thermal conductivity of the rod material as 15 W/m-°Ca)142b)143Correct answer is between '142,143'. Can you explain this answer?
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A tapered stainless steel rod, perfectly insulated on the curved surface, has end diameters of 6 cm and 12 cm respectively, and is 20 cm long. The thicker end is fixed to a hot wall and the thinner end is maintained at 25°C. The steady state rate of heat loss through the rod is estimated to be 50W. Calculate the temperature at the hot end of the rod. Take thermal conductivity of the rod material as 15 W/m-°Ca)142b)143Correct answer is between '142,143'. Can you explain this answer? for Chemical Engineering 2024 is part of Chemical Engineering preparation. The Question and answers have been prepared according to the Chemical Engineering exam syllabus. Information about A tapered stainless steel rod, perfectly insulated on the curved surface, has end diameters of 6 cm and 12 cm respectively, and is 20 cm long. The thicker end is fixed to a hot wall and the thinner end is maintained at 25°C. The steady state rate of heat loss through the rod is estimated to be 50W. Calculate the temperature at the hot end of the rod. Take thermal conductivity of the rod material as 15 W/m-°Ca)142b)143Correct answer is between '142,143'. Can you explain this answer? covers all topics & solutions for Chemical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A tapered stainless steel rod, perfectly insulated on the curved surface, has end diameters of 6 cm and 12 cm respectively, and is 20 cm long. The thicker end is fixed to a hot wall and the thinner end is maintained at 25°C. The steady state rate of heat loss through the rod is estimated to be 50W. Calculate the temperature at the hot end of the rod. Take thermal conductivity of the rod material as 15 W/m-°Ca)142b)143Correct answer is between '142,143'. Can you explain this answer?.
A tapered stainless steel rod, perfectly insulated on the curved surface, has end diameters of 6 cm and 12 cm respectively, and is 20 cm long. The thicker end is fixed to a hot wall and the thinner end is maintained at 25°C. The steady state rate of heat loss through the rod is estimated to be 50W. Calculate the temperature at the hot end of the rod. Take thermal conductivity of the rod material as 15 W/m-°Ca)142b)143Correct answer is between '142,143'. Can you explain this answer? for Chemical Engineering 2024 is part of Chemical Engineering preparation. The Question and answers have been prepared according to the Chemical Engineering exam syllabus. Information about A tapered stainless steel rod, perfectly insulated on the curved surface, has end diameters of 6 cm and 12 cm respectively, and is 20 cm long. The thicker end is fixed to a hot wall and the thinner end is maintained at 25°C. The steady state rate of heat loss through the rod is estimated to be 50W. Calculate the temperature at the hot end of the rod. Take thermal conductivity of the rod material as 15 W/m-°Ca)142b)143Correct answer is between '142,143'. Can you explain this answer? covers all topics & solutions for Chemical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A tapered stainless steel rod, perfectly insulated on the curved surface, has end diameters of 6 cm and 12 cm respectively, and is 20 cm long. The thicker end is fixed to a hot wall and the thinner end is maintained at 25°C. The steady state rate of heat loss through the rod is estimated to be 50W. Calculate the temperature at the hot end of the rod. Take thermal conductivity of the rod material as 15 W/m-°Ca)142b)143Correct answer is between '142,143'. Can you explain this answer?.
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A tapered stainless steel rod, perfectly insulated on the curved surface, has end diameters of 6 cm and 12 cm respectively, and is 20 cm long. The thicker end is fixed to a hot wall and the thinner end is maintained at 25°C. The steady state rate of heat loss through the rod is estimated to be 50W. Calculate the temperature at the hot end of the rod. Take thermal conductivity of the rod material as 15 W/m-°Ca)142b)143Correct answer is between '142,143'. Can you explain this answer?, a detailed solution for A tapered stainless steel rod, perfectly insulated on the curved surface, has end diameters of 6 cm and 12 cm respectively, and is 20 cm long. The thicker end is fixed to a hot wall and the thinner end is maintained at 25°C. The steady state rate of heat loss through the rod is estimated to be 50W. Calculate the temperature at the hot end of the rod. Take thermal conductivity of the rod material as 15 W/m-°Ca)142b)143Correct answer is between '142,143'. Can you explain this answer? has been provided alongside types of A tapered stainless steel rod, perfectly insulated on the curved surface, has end diameters of 6 cm and 12 cm respectively, and is 20 cm long. The thicker end is fixed to a hot wall and the thinner end is maintained at 25°C. The steady state rate of heat loss through the rod is estimated to be 50W. Calculate the temperature at the hot end of the rod. Take thermal conductivity of the rod material as 15 W/m-°Ca)142b)143Correct answer is between '142,143'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A tapered stainless steel rod, perfectly insulated on the curved surface, has end diameters of 6 cm and 12 cm respectively, and is 20 cm long. The thicker end is fixed to a hot wall and the thinner end is maintained at 25°C. The steady state rate of heat loss through the rod is estimated to be 50W. Calculate the temperature at the hot end of the rod. Take thermal conductivity of the rod material as 15 W/m-°Ca)142b)143Correct answer is between '142,143'. Can you explain this answer? tests, examples and also practice Chemical Engineering tests.
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