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The unit of thermal conductivity is :...

The unit of thermal conductivity is :

A

`W m^(-1) K^(-1)`

B

`J m^(-1) K^(-1)`

C

`J m^(-1) K^(-1)`

D

`W m K^(-1)`

Text Solution

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The correct Answer is:
To find the unit of thermal conductivity, we start with the formula for thermal conductivity (K): \[ K = \frac{Q \cdot D}{A \cdot \Delta T} \] Where: - \( Q \) is the amount of heat transferred (measured in Joules or Watts), - \( D \) is the distance between the two isothermal planes (measured in meters), - \( A \) is the area of the surface (measured in square meters), - \( \Delta T \) is the temperature difference (measured in Kelvin). ### Step 1: Identify the units of each variable - The unit of heat transferred \( Q \) is Watts (W). - The unit of distance \( D \) is meters (m). - The unit of area \( A \) is square meters (m²). - The unit of temperature difference \( \Delta T \) is Kelvin (K). ### Step 2: Substitute the units into the formula Now we substitute these units into the formula for thermal conductivity: \[ K = \frac{Q \cdot D}{A \cdot \Delta T} \] Substituting the units: \[ K = \frac{W \cdot m}{m^2 \cdot K} \] ### Step 3: Simplify the expression Now we simplify the expression: \[ K = \frac{W \cdot m}{m^2 \cdot K} = \frac{W}{m \cdot K} \] ### Final Result Thus, the unit of thermal conductivity \( K \) is: \[ K = \frac{W}{m \cdot K} \] This can also be written as: \[ K = \text{W/m·K} \] ### Conclusion The unit of thermal conductivity is **Watt per meter Kelvin (W/m·K)**. ---

To find the unit of thermal conductivity, we start with the formula for thermal conductivity (K): \[ K = \frac{Q \cdot D}{A \cdot \Delta T} \] Where: - \( Q \) is the amount of heat transferred (measured in Joules or Watts), - \( D \) is the distance between the two isothermal planes (measured in meters), - \( A \) is the area of the surface (measured in square meters), ...
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