The related equations are $Q = m c (T_{2} - T_{1}), ℓ_{1} = ℓ_{0} [1 + α (T_{2} - T_{1})]$ and $P V = n R T$ , where the symbols have their usual meanings. Find the dimensions of
(A) specific heat capacity $(C)$ (B) coefficient of linear expansion $(α)$ and $(C)$ the gas constant $(R)$ .

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Solution

(i) $c = \frac{Q}{m [T_{2} - T_{1}]}$
Dimension of $c = \frac{[M^{1} L^{2} T^{- 2}]}{[M^{1} L^{0} T^{0}] [M^{0} L^{0} T^{0} K^{1}]}$
$= [L^{2} T^{- 2} K^{- 1}]$
(ii) $α = \frac{ℓ_{1} - ℓ_{0}}{ℓ_{0} (T_{2} - T_{1})}$
$\Rightarrow$ Dimension of $α = \frac{[M^{0} L^{1} T^{0}]}{[M^{0} L^{1} T^{0}] [M^{0} L^{0} T^{0} K^{1}]}$ = $[K^{1}]$
(iii) $R = \frac{P V}{n T} = \frac{[M^{- 1} L^{- 1} T^{- 2}] [L^{3}]}{[m o l] [K]} = [M^{1} L^{2} T^{- 2} K^{- 1} m o l^{- 1}]$

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Similar questions

Find the dimensions of

(a) the specific heat capacity c,

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Some of the equations involving these quatities are $Q = m c (T_{2} - T_{1}), l_{1} = l_{0} [1 + α (T_{2} - T_{1})]$ and PV = nRT.

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1

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