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Real Gases

The dimension...

Question

The dimensional formula of $R T$ is same as that of:

energy

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force

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specific heat

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latent heat

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Solution

The correct option is A energy
The vander Waals gas equation is $(\begin{matrix} P + \frac{a}{V^{2}} \end{matrix}) (V - b) = R T$

where $P$ is the pressure, $V$ is molar volume and $T$ is the temperature of the given sample of gas. $R$ is called mola gas constant, $a$ and $b$ are called vander Waals constants.

$(\begin{matrix} P + \frac{a}{V^{2}} \end{matrix}) (V - b) = R T$ ,

$P V + \frac{a}{V} - P b - \frac{a b}{V^{2}} = R T$

So, $[P V] = [R T]; [\frac{a}{V}] = [R T]; [P b] = [R T]; [\frac{a b}{V^{2}}] = [R T]$

$[R T] = [P V] = (M L^{- 1} T^{- 2}) (L^{3}) = M L^{2} T^{- 2} = [E n e r g y]$

Since energy has dimension of $E = M g h = M L^{2} T^{- 2}$

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Similar questions

R T

P = \frac{R T}{V - b} e^{\frac{- a V}{R T}} .

a

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P = \frac{R T}{V - b} e^{\frac{a V}{R T}}

V = v o l u m e, P = p r e s s u r e, R =

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Dimensional formula of stress is same as that of

P = \frac{R T}{v - b} e^{⎛ ⎝ \frac{- a V}{R T} ⎞ ⎠}

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