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Q)

The intercept of plots of log V vs log T curves at constant pressure P for 1 mole gas will be

$(a)\;log \large\frac{P}{R}\qquad(b)\;log \large\frac{-P}{R}\qquad(c)\;log \large\frac{R}{P}\qquad(d)\;log \large\frac{-R}{P}$

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A)
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  • The behaviour of gases has been expressed in terms of various gas laws obtained experimentally i.e Boyle's law , Charles law , Pressure-temperature law , Dalton's law of partial pressure , Graham's law of diffusion and Avogadro's hypothesis . Later on Maxwell derived kinetic equation $PV = \large\frac{1}{3}mnu^2$ , theoretically by assuming the concept of molecules and their motion . The term u represents root mean square speed of molecule.
PV = nRT
$log V = log T + log \large\frac{nR}{P}$ at constant pressure
Or $log V = log T + log \large\frac{nR}{P}$
Thus plot of log V vs log T for 1 mole
give intercept equal to $log \large\frac{R}{P}$
Hence answer is (C)
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