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Standard XII

Physics

Dimensional Analysis

The dimension...

Question

The dimensional equation for the universal gas constant is

[M^{1} L^{1} T^{- 2} K^{- 1} m o l^{- 1}]

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[M^{2} L^{2} T^{- 2} K^{- 1} m o l^{- 1}]

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[M^{1} L^{2} T^{- 2} K^{- 1} m o l^{- 1}]

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[M^{2} L^{1} T^{- 2} K^{- 1} m o l^{- 1}]

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Solution

The correct option is C $[M^{1} L^{2} T^{- 2} K^{- 1} m o l^{- 1}]$
Universal gas consatnt, $[R] = \frac{[P r e s s u r e] [V o l u m e]}{[N u m b e r o f m o l e s] [T e m p e r a t u r e]}$

$= \frac{[M L^{- 1} T^{- 2}] [L^{3}]}{m o l \times K}$

$= [M L^{2} T^{- 2} K^{- 1} m o l^{- 1}$ ]

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The dimensional equation for the universal gas constant is

The correct option is C [M1L2T−2K−1mol−1]Universal gas consatnt, [R]=[Pressure][Volume][Numberofmoles][Temperature]=[ML−1T−2][L3]mol×K=[ML2T−2K−1mol−1]

The correct option is C $[M^{1} L^{2} T^{- 2} K^{- 1} m o l^{- 1}]$
Universal gas consatnt, $[R] = \frac{[P r e s s u r e] [V o l u m e]}{[N u m b e r o f m o l e s] [T e m p e r a t u r e]}$

$= \frac{[M L^{- 1} T^{- 2}] [L^{3}]}{m o l \times K}$

$= [M L^{2} T^{- 2} K^{- 1} m o l^{- 1}$ ]