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Standard XII

Physics

Dimensional Analysis

The equation ...

Question

The equation of state of a gas is given by $(\begin{matrix} P + \frac{a}{v^{3}} \end{matrix}) (V - b^{2}) = c T$ , where P, V, T are pressure, volume and temperature respectively, and a, b, c are constants. The dimensions of a and b are respectively

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

and

L^{3 / 2}

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

and

L^{3}

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

and

L

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

and

L^{3 / 2}

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Solution

The correct option is A $M L^{8} T^{- 2}$ and $L^{3 / 2}$
The dimensions of $\frac{a}{v^{3}}$ must be that of pressure.
Dimension of pressure are $[M L^{- 1} T^{- 2}]$
Hence dimension of $a$ is $[M L^{- 1 + 3 * 3} T^{- 2}] = [M L^{8} T^{- 2}]$
The dimension of $b^{2}$ must be that of volume.
Hence $[b^{2}] = [L^{3}]$
$⟹ [b] = [L^{3 / 2}]$

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The equation of state of a gas is given by (P+av3)(V−b2)=cT, where P, V, T are pressure, volume and temperature respectively, and a, b, c are constants. The dimensions of a and b are respectively

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The equation of state of a gas is given by $(\begin{matrix} P + \frac{a}{v^{3}} \end{matrix}) (V - b^{2}) = c T$ , where P, V, T are pressure, volume and temperature respectively, and a, b, c are constants. The dimensions of a and b are respectively