The variation of thermal conductivity of a metal with temperature is often correlated using an expression of the form K = K₀ + at. where, K is the thermal conductivity and T is the temperature (in °K). The units of 'a' in SI system will be

ANS:C - W/m.k²

The expression provided correlates thermal conductivity K with temperature T using the equation K=K0​+at, where:

• K is the thermal conductivity.
• 0K0​ is the thermal conductivity at =0T=0.
• a is a constant.
• t is the temperature (in Kelvin).

Since thermal conductivity K is typically measured in watts per meter per Kelvin (W/m⋅K), and temperature t is in Kelvin, the units of a need to match to ensure the equation is dimensionally consistent. The units of a can be determined by rearranging the equation: K−K0​=at a=tK−K0​​ From this, we can see that the units of a are: 2KW/m⋅K−W/m⋅K​=m⋅K2W​ So, the correct answer is W/m·K^2.