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6.0 kJ of conduction heat transfer has to take place in 10 minutes from one end to other end of a metallic cylinder of 10 cm2 cross-sectional area, length 1 meter and thermal conductivity as 100 W/mK. What is the temperature difference between the two ends of the cylindrical bar?
- a)80°C
- b)100°C
- c)120°C
- d)160°C
Correct answer is option 'B'. Can you explain this answer?
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6.0 kJ of conduction heat transfer has to take place in 10 minutes fro...
Ans. (b)
or
or dt = 1000C
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6.0 kJ of conduction heat transfer has to take place in 10 minutes fro...
Given data:
- Conduction heat transfer: 6.0 kJ
- Cross-sectional area of the cylinder: 10 cm²
- Length of the cylinder: 1 meter
- Thermal conductivity of the material: 100 W/mK
To find: Temperature difference between the two ends of the cylindrical bar
We can use the formula for conduction heat transfer:
Q = (k * A * ΔT) / L
Where:
- Q is the heat transfer (in Joules)
- k is the thermal conductivity of the material (in W/mK)
- A is the cross-sectional area of the cylinder (in m²)
- ΔT is the temperature difference (in K)
- L is the length of the cylinder (in meters)
Let's convert all the given values to SI units:
- Conduction heat transfer: 6.0 kJ = 6000 J
- Cross-sectional area of the cylinder: 10 cm² = 0.001 m²
- Length of the cylinder: 1 meter
- Thermal conductivity of the material: 100 W/mK
Now, we can rearrange the formula to solve for ΔT:
ΔT = (Q * L) / (k * A)
Substituting the given values:
ΔT = (6000 J * 1 m) / (100 W/mK * 0.001 m²)
ΔT = 60 K
Therefore, the temperature difference between the two ends of the cylindrical bar is 60 K.
Hence, the correct answer is option 'B' (100°C).
- Conduction heat transfer: 6.0 kJ
- Cross-sectional area of the cylinder: 10 cm²
- Length of the cylinder: 1 meter
- Thermal conductivity of the material: 100 W/mK
To find: Temperature difference between the two ends of the cylindrical bar
We can use the formula for conduction heat transfer:
Q = (k * A * ΔT) / L
Where:
- Q is the heat transfer (in Joules)
- k is the thermal conductivity of the material (in W/mK)
- A is the cross-sectional area of the cylinder (in m²)
- ΔT is the temperature difference (in K)
- L is the length of the cylinder (in meters)
Let's convert all the given values to SI units:
- Conduction heat transfer: 6.0 kJ = 6000 J
- Cross-sectional area of the cylinder: 10 cm² = 0.001 m²
- Length of the cylinder: 1 meter
- Thermal conductivity of the material: 100 W/mK
Now, we can rearrange the formula to solve for ΔT:
ΔT = (Q * L) / (k * A)
Substituting the given values:
ΔT = (6000 J * 1 m) / (100 W/mK * 0.001 m²)
ΔT = 60 K
Therefore, the temperature difference between the two ends of the cylindrical bar is 60 K.
Hence, the correct answer is option 'B' (100°C).
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