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  • <img alt="\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cleft%28%5Cmathrm%7BP%7D&plus;%5Cfra

\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}   represents the equation of state of some gases. Where P is the pressure, V is the volume, T is the temperature and a, b, R are the constants. The physical quantity, which has  dimensional formula as that of  \frac{b^{2}}{a}  will be:

Option: 1

 Compressibility


Option: 2

 Energy density
 


Option: 3

 Modulus of rigidity


Option: 4

Bulk modulus


Answers (1)

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\begin{aligned} & {[\mathrm{b}]=\left[\mathrm{L}^3\right]} \\ & \begin{aligned} {[\mathrm{a}] } & =\left[\mathrm{PV}^2\right] \\ & =\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]\left[\mathrm{L}^6\right] \\ & =\left[\mathrm{ML}^5 \mathrm{~T}^{-2}\right] \end{aligned} \\ & \frac{\left[\mathrm{b}^2\right]}{[\mathrm{a}]}=\frac{\left[\mathrm{L}^6\right]}{\left[\mathrm{ML}^5 \mathrm{~T}^{-2}\right]}=\left[\mathrm{M}^{-1} \mathrm{~L}^1 \mathrm{~T}^2\right] \end{aligned}

Posted by

Gautam harsolia

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