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1.Units, Dimensions and Measurement
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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
$\frac{m}{Q \Delta T}$
Solution
(b)
$Q=m^a s^b \theta^c$
$\left[ ML ^2 T ^{-2}\right]=\left[ M ^2\right]\left[ L ^{2 b} T ^{-2 b} K ^{-b}\right]\left[ K ^{ C }\right]$
$\Rightarrow a=1$,
$2 b=2 \Rightarrow b=1$
$-b+c=0$
$\Rightarrow b=c \Rightarrow c=1$
$Q=m s \Delta T$
$\Rightarrow s=\frac{Q}{m \Delta T}$
Standard 11
Physics
