Question

Derive the dimensions of specific heat that is defined as the amount of heat required to elevate the temperature of an object of mass 1 kg by 1 degree Celcius.

Answer 1

Answer:

Dimension of specific heat will be $=L^2T^{-2}\Theta ^{-1}$

Explanation:

We know that heat $Q=mc\Delta T$, Q is heat generated, m is mass, c is specific heat and $\Delta T$ is temperature difference

From formula we can write $c=\frac{Q}{m\times \Delta T}$

Now unit of Q is joule or N-m

Newton can be written as $kgm/sec^2$

So unit of Q is $kgm^2/sec^2$

For dimension we use M for kg, L for meter(m) ,T for sec and $\Theta$ for temperature

So dimension of Q is $ML^2T^{-2}$

So dimension of specific heat will be $\frac{ML^2T^{-2}}{M\Theta }=L^2T^{-2}\Theta ^{-1}$