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