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The hollow metallic sphere of radius 20cm surrounds a concentric metallic sphere of radius 5cm. The space between the two spheres is filled with a non metallic material. The inner and Outer sphere are maintained at 50 degree Centigrade and 10 degree centigrade respectively and it is found that 100 joule of heat passes from inner sphere to the outer sphere per second. Find the thermal conductivity of material between the spheres (in watt/ metre Kelvin)?
Most Upvoted Answer
The hollow metallic sphere of radius 20cm surrounds a concentric metal...
Given information:
- Inner sphere radius (r1) = 5 cm = 0.05 m
- Outer sphere radius (r2) = 20 cm = 0.2 m
- Temperature of inner sphere (T1) = 50°C = 323 K
- Temperature of outer sphere (T2) = 10°C = 283 K
- Heat transfer rate (Q) = 100 J/s
Concept:
The heat transfer rate between two spheres can be calculated using the formula:
Q = (4πkAΔT)/d
where:
- Q is the heat transfer rate
- k is the thermal conductivity of the material
- A is the surface area of the sphere
- ΔT is the temperature difference between the two spheres
- d is the distance between the two spheres
Calculation:
1. Surface Area of the Inner Sphere (A1):
A1 = 4πr1²
2. Surface Area of the Outer Sphere (A2):
A2 = 4πr2²
3. Area for Heat Transfer (A):
A = A1 - A2
4. Distance between the Spheres (d):
d = r2 - r1
5. Temperature Difference (ΔT):
ΔT = T1 - T2
6. Substituting the values in the heat transfer equation:
Q = (4πkAΔT)/d
7. Rearranging the equation to solve for k:
k = (Q * d)/(4πAΔT)
Final Calculation:
Substituting the given values:
k = (100 * 0.15)/(4π * (4π * 0.05² - 4π * 0.2²) * (323 - 283))
Simplifying the equation:
k ≈ 0.21 W/(m·K)
Final Answer:
The thermal conductivity of the material between the spheres is approximately 0.21 W/(m·K).
- Inner sphere radius (r1) = 5 cm = 0.05 m
- Outer sphere radius (r2) = 20 cm = 0.2 m
- Temperature of inner sphere (T1) = 50°C = 323 K
- Temperature of outer sphere (T2) = 10°C = 283 K
- Heat transfer rate (Q) = 100 J/s
Concept:
The heat transfer rate between two spheres can be calculated using the formula:
Q = (4πkAΔT)/d
where:
- Q is the heat transfer rate
- k is the thermal conductivity of the material
- A is the surface area of the sphere
- ΔT is the temperature difference between the two spheres
- d is the distance between the two spheres
Calculation:
1. Surface Area of the Inner Sphere (A1):
A1 = 4πr1²
2. Surface Area of the Outer Sphere (A2):
A2 = 4πr2²
3. Area for Heat Transfer (A):
A = A1 - A2
4. Distance between the Spheres (d):
d = r2 - r1
5. Temperature Difference (ΔT):
ΔT = T1 - T2
6. Substituting the values in the heat transfer equation:
Q = (4πkAΔT)/d
7. Rearranging the equation to solve for k:
k = (Q * d)/(4πAΔT)
Final Calculation:
Substituting the given values:
k = (100 * 0.15)/(4π * (4π * 0.05² - 4π * 0.2²) * (323 - 283))
Simplifying the equation:
k ≈ 0.21 W/(m·K)
Final Answer:
The thermal conductivity of the material between the spheres is approximately 0.21 W/(m·K).
Community Answer
The hollow metallic sphere of radius 20cm surrounds a concentric metal...
That's very typical question ?
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The hollow metallic sphere of radius 20cm surrounds a concentric metallic sphere of radius 5cm. The space between the two spheres is filled with a non metallic material. The inner and Outer sphere are maintained at 50 degree Centigrade and 10 degree centigrade respectively and it is found that 100 joule of heat passes from inner sphere to the outer sphere per second. Find the thermal conductivity of material between the spheres (in watt/ metre Kelvin)?
Question Description
The hollow metallic sphere of radius 20cm surrounds a concentric metallic sphere of radius 5cm. The space between the two spheres is filled with a non metallic material. The inner and Outer sphere are maintained at 50 degree Centigrade and 10 degree centigrade respectively and it is found that 100 joule of heat passes from inner sphere to the outer sphere per second. Find the thermal conductivity of material between the spheres (in watt/ metre Kelvin)? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The hollow metallic sphere of radius 20cm surrounds a concentric metallic sphere of radius 5cm. The space between the two spheres is filled with a non metallic material. The inner and Outer sphere are maintained at 50 degree Centigrade and 10 degree centigrade respectively and it is found that 100 joule of heat passes from inner sphere to the outer sphere per second. Find the thermal conductivity of material between the spheres (in watt/ metre Kelvin)? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The hollow metallic sphere of radius 20cm surrounds a concentric metallic sphere of radius 5cm. The space between the two spheres is filled with a non metallic material. The inner and Outer sphere are maintained at 50 degree Centigrade and 10 degree centigrade respectively and it is found that 100 joule of heat passes from inner sphere to the outer sphere per second. Find the thermal conductivity of material between the spheres (in watt/ metre Kelvin)?.
The hollow metallic sphere of radius 20cm surrounds a concentric metallic sphere of radius 5cm. The space between the two spheres is filled with a non metallic material. The inner and Outer sphere are maintained at 50 degree Centigrade and 10 degree centigrade respectively and it is found that 100 joule of heat passes from inner sphere to the outer sphere per second. Find the thermal conductivity of material between the spheres (in watt/ metre Kelvin)? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The hollow metallic sphere of radius 20cm surrounds a concentric metallic sphere of radius 5cm. The space between the two spheres is filled with a non metallic material. The inner and Outer sphere are maintained at 50 degree Centigrade and 10 degree centigrade respectively and it is found that 100 joule of heat passes from inner sphere to the outer sphere per second. Find the thermal conductivity of material between the spheres (in watt/ metre Kelvin)? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The hollow metallic sphere of radius 20cm surrounds a concentric metallic sphere of radius 5cm. The space between the two spheres is filled with a non metallic material. The inner and Outer sphere are maintained at 50 degree Centigrade and 10 degree centigrade respectively and it is found that 100 joule of heat passes from inner sphere to the outer sphere per second. Find the thermal conductivity of material between the spheres (in watt/ metre Kelvin)?.
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