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Standard XII

Physics

Dimensional Analysis

The Van der W...

Question

The Van der Waal's equation of $^{'} n^{'}$ moles of a real gas is
$(P + \frac{a}{V^{2}}) (V - b) = n R T$
Where $P$ is pressure, $V$ is volume, $T$ is absolute temperature, $R$ is molar gas constant and $a, b, c$ are Van der Waal constants. The dimensional formula for $a b$ is:

[

M L^{8} T^{- 2}

]

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[

M L^{6} T^{- 2}

]

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[

M L^{4} T^{- 2}

]

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[

M L^{2} T^{- 2}

]

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Solution

The correct option is A [ $M L^{8} T^{- 2}$ ]
Since, the dimensions of $P$ must be same as $\frac{a}{V^{2}}$ ,
Hence,
$\frac{[a]}{L^{6}} = [M L^{- 1} T^{- 2}]$

$[a] = [M L^{5} T^{- 2}]$

Also, dimension of $b$ must be same as that of $V$ . Hence, $[b] = L^{3}$ .

Thus, $[a b] = [M L^{8} T^{- 2}]$

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Similar questions

Q. The Van der Wall equation for

1

mole of a real gas is

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

where

P

is the pressure,

V

is the volume,

T

is the absolute temperature,

R

is the molar gas constant and

a, b

are Van der Wall constants. The dimensions of

a

are the same as those of :

Comprhension:
The van der Waal's 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 molar gas constant,

a

and

b

are called van der Waal's constants.

The dimensional formula for

a

is same as that for

Q. The vander Waal's equation of a gas is

(P + \frac{a}{V^{2}}) (V - b) = n R T

where

P, V, R, T

and

n

represent the pressure, volume, universal gas constant, absolute temperature and number of moles of a gas respectively,

a

and

b

are constants. The ratio

\frac{b}{a}

will have the following dimensional formula.

Q. The Van der Waal's equation of state for some gases can be expressed as:

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

where P is the pressure, V is the molar volume, and T is the absolute temperature of the given sample of gas and a,b and R are constants.
The dimensional representation of ab/RT is

Q. The Van der Waal's equation of state for some gases can be expressed as:

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

where P is the pressure, V is the molar volume, and T is the absolute temperature of the given sample of gas and a,b and R are constants.
The dimensions of constant b are

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The Van der Waal's equation of ′n′ moles of a real gas is(P+aV2)(V−b)=nRTWhere P is pressure, V is volume, T is absolute temperature, R is molar gas constant and a,b,c are Van der Waal constants. The dimensional formula for ab is:

The correct option is A [ML8T−2]Since, the dimensions of P must be same as aV2, Hence,[a]L6=[ML−1T−2][a]=[ML5T−2]Also, dimension of b must be same as that of V. Hence, [b]=L3.Thus, [ab]=[ML8T−2]

The Van der Waal's equation of $^{'} n^{'}$ moles of a real gas is
$(P + \frac{a}{V^{2}}) (V - b) = n R T$
Where $P$ is pressure, $V$ is volume, $T$ is absolute temperature, $R$ is molar gas constant and $a, b, c$ are Van der Waal constants. The dimensional formula for $a b$ is:

The correct option is A [ $M L^{8} T^{- 2}$ ]
Since, the dimensions of $P$ must be same as $\frac{a}{V^{2}}$ ,
Hence,
$\frac{[a]}{L^{6}} = [M L^{- 1} T^{- 2}]$

$[a] = [M L^{5} T^{- 2}]$

Also, dimension of $b$ must be same as that of $V$ . Hence, $[b] = L^{3}$ .

Thus, $[a b] = [M L^{8} T^{- 2}]$