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Standard XII

Physics

1st Law of Thermodynamics

The equation ...

Question

The equation of state of a real gas is given by $(P = \frac{a}{V^{2}}) (V - b) = R T$ , where P, V and T are pressure, volume and temperature respectively and R is the universal gas constant. The dimensions of the constant a in the given equation is _______.

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

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M L^{5} T^{- 2}

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M L^{7} T^{- 2}

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

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Solution

The correct option is B $M L^{5} T^{- 2}$ .
Dimension of P = Dimension of $(\frac{a}{V^{2}})$
$\Rightarrow M L^{- 1} T^{- 2} = \frac{Dimension of a}{L^{6}}$
$\Rightarrow Dimension of a = M L^{5} T^{- 2}$
Hence, option B is correct.

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The equation of state of a real gas is given by (P=aV2)(V−b)=RT, where P, V and T are pressure, volume and temperature respectively and R is the universal gas constant. The dimensions of the constant a in the given equation is _______.

The correct option is B ML5T−2.Dimension of P = Dimension of (aV2)⇒ML−1T−2= Dimension of aL6⇒Dimension of a=ML5T−2Hence, option B is correct.

The equation of state of a real gas is given by $(P = \frac{a}{V^{2}}) (V - b) = R T$ , where P, V and T are pressure, volume and temperature respectively and R is the universal gas constant. The dimensions of the constant a in the given equation is _______.

The correct option is B $M L^{5} T^{- 2}$ .
Dimension of P = Dimension of $(\frac{a}{V^{2}})$
$\Rightarrow M L^{- 1} T^{- 2} = \frac{Dimension of a}{L^{6}}$
$\Rightarrow Dimension of a = M L^{5} T^{- 2}$
Hence, option B is correct.