Which one of the following relationship is correct

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$PV = \frac{3}{2} KT$

$K . E = \frac{2}{3} KT$

$Z = \frac{nRT}{PV}$

$\frac{PV}{T} = \frac{2}{3} K$

answer is D.

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Detailed Solution

The kinetic gas equation is given as

$consider PV = \frac{1}{3} {mnc}^{2}, (n = N)$

$PV = \frac{1}{3} {mNC}^{2}$

$PV = \frac{1}{3} {MC}^{2} (Since, M = m \times N)$

$\Rightarrow PV = \frac{2}{3} \times \frac{1}{2} {MC}^{2}$

$PV = \frac{2}{3} K . E (Since K . E = \frac{1}{2} {MC}^{2})$

$PV = \frac{2}{3} K . T we know that K . EαT and K . E = K . T$ $\frac{PV}{T} = \frac{2}{3} K$

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