Find the dimensions

Question:

Find the dimensions of

a)the specific heat capacity $c$

b)the coefficient of linear expansion a,

c) the gas constant R

Solution:

a) Specific heat constant $c=Q / m\left(T_{2}-T_{1}\right)=\left[M^{2} T^{-2}\right] /[M][\theta]=\left[L^{2} T^{-2} \theta^{-1}\right]$

b) Coefficient of linear expansion $\alpha=\frac{[L]}{[L][\theta]}=[\theta]$

c) Gas constant $=\mathrm{R}=\mathrm{PV} / \mathrm{nT}=\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]\left[\mathrm{L}^{3}\right][\mathrm{mol}][\theta]=\left[\mathrm{ML}^{2} \mathrm{~T}^{-2} \theta^{-1}\left(\mathrm{~mol}^{-1}\right]\right.$