Explain how SI unit of coefficient of thermal conductivity be obtained as W/m °C or W/m K.

1. Consider equation, \(\frac{Q}{t}=\frac{kA(T_1-T_2)}{x}\)

2. The quantity Q/t, denoted by P_cond, is the time rate of heat flow (i.e. heat flow per second) from the hotter face to the colder face, at right angles to the faces.

3. Its SI unit is watt (W).

4. SI unit of k can therefore be written as W m^-1°C^-1 or W m^-1 K^-1.

[Note: Above equation, using calculus can be written as, \(\frac{dQ}{dt}\) = – kA \(\frac{dT}{dx}\), where \(\frac{dT}{dx}\) is the temperature gradient. The negative sign indicates that heat flow is in the direction of decreasing temperature. If A = 1 m² and \(\frac{dT}{dx}\) = 1, then \(\frac{dQ}{dt}\) = k.]