Question

The dimensional formula for thermal resistance is :

• A. $M ^{-1} L ^{-2} T ^{3} \theta$
• B. $M ^{-1} L ^{-2} T ^{3} \theta$
• C. $ML ^{-2} T ^{2} \theta$
• D. $ML ^{-2} T ^{-2} \theta^{-1}$

Answer 1

Answer: (A)

When thermal conductivity is $K$,
thermal resistivity is $\frac{1}{K}$,
then thermal resistance $R=\frac{1 \times L}{K A}$
Now heat conducted is given by
$\frac{Q_{1}}{t}=\theta_{1} \frac{k A\left(\theta_{1}-\theta_{2}\right)}{L}=\frac{\theta_{1}-\theta_{2}}{R}$
Therefore, dimensions of $R =$ dimensions of
$\frac{\left(\theta_{1}-\theta_{2}\right) t}{Q}$
$=\frac{\theta T}{M \times\left(L^{2} T^{-2} \theta^{-1}\right)}$
$=M^{-1} L^{-2} T^{3} \theta$