What are the dimensions of gas constant?

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

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[M^{0} L T^{- 2} K^{- 1}]

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

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[M^{0} L^{2} T^{- 2} K^{- 1}]

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Solution

The correct option is A $[M L^{2} T^{- 2} K^{- 1} m o l^{- 1}]$
We know $P V = n R T$
$R = \frac{P V}{n T} = \frac{F o r c e \times V o l u m e}{n T \times a r e a}$
$= \frac{[{M L T}^{- 2} L^{3}]}{[m o l K \times L^{2}]}$
$R = [{M L}^{2} T^{- 2} K^{- 1} {m o l}^{- 1}]$

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Similar questions

P V = n R T

R

	Column I (Units)		Column II (Dimensional formulae)
(A)	Pa s	(p)	$[M^{0} L^{2} T^{- 2} K^{- 1}]$
(B)	N m K $^{- 1}$	(q)	$[M L T^{- 3} K^{- 1}]$
(C)	J kg $^{- 1}$ K $^{- 1}$	(r)	$[M L^{- 1} T^{- 1}]$
(D)	W m $^{- 1}$ K $^{- 1}$	(s)	$[M L^{2} T^{- 2} K^{- 1}]$

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

(\frac{d Q}{d t} = - K A \frac{d T}{d x})

d Q

d t

K

A

d T

d x

f (x) = c o s (\frac{π}{x}), x \neq 0

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