Question

Find SI units of thermal resistance.

Answer 1

Hint:An easy way would be to use the formula for thermal resistance and instead of putting values, put the units of respective quantities in the formula. After simplification, we will be left with the unit of Thermal Resistance.

Formula Used:
Thermal Resistance, $R = \dfrac{{\Delta x}}{{A \times k}}$
Where, $\Delta x$ is the thickness of the sample (measured parallel the direction of flow of heat), $k$ is the thermal conductivity of the sample, $A$ is the area of cross section (perpendicular to the direction of flow of heat)

Complete Step by Step Solution:
We have the formula of thermal resistance as $R = \dfrac{{\Delta x}}{{A \times k}}$ where, $\Delta x$ is the thickness of the sample (measured parallel the direction of flow of heat), $k$ is the thermal conductivity of the sample, $A$ is the area of cross section (perpendicular to the direction of flow of heat)
Now we know that the SI unit for thickness is metres $(m)$ , for Thermal Conductivity is Watt per Kelvin-Metre $(W/Km)$ , and for cross sectional area is metre square $({m^2})$
Putting these SI units in the respective places, we get $R = \dfrac{m}{{{m^2} \times \dfrac{W}{{m \times K}}}}$
Now we will simplify it as \[R = \dfrac{{{m^2} \times K}}{{{m^2} \times W}}\]
As we can clearly see, ${m^2}$ is in the numerator as well as the denominator, it will get cancelled out
Hence, we are left with \[R = \dfrac{K}{W}\] . This is the required answer.

Therefore, the SI unit for thermal resistance is Kelvin per Watt $(K/W)$

Note:Make sure you use the SI units of quantities in the formula, like in this case in the formula of thermal resistance, to get the final answer as the SI units. If you use cgs units, you will get the final answer in the cgs system only.