Question

The amount of heat energy $Q$, used to heat up a substance depends on its mass $m$, its specific heat capacity $(s)$ and the change in temperature $\Delta T$ of the substance. Using dimensional method, find the expression for $s$ is (Given that $\left.[s]=\left[L^{2} T^{-2} K^{-1}\right]\right)$ is

• A. $Q m \Delta T$
• B. $\frac{Q}{m \Delta T}$
• C. $\frac{Q m}{\Delta T}$
• D. $\frac{m}{Q \Delta T}$

Answer 1

Answer: (B)

$Q=m^{a} s^{b} \theta^{c}$
$\left[ ML ^{2} T ^{-2}\right]=\left[ M ^{9}\right]\left[ L ^{2 b} T ^{-2 b} K ^{-b}\right]\left[ K ^{ c }\right]$
$\Rightarrow a=1,\,\,2 b=2 \Rightarrow b=1$
$-b +c=0$
$\Rightarrow b=c \Rightarrow c=1$
$Q=m s \Delta T$
$\Rightarrow s=\frac{Q}{m \Delta T}$