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A cylinder of capacity 20 litres is filled with Helium gas. The total average kinetic energy of translatory motion of its atoms is $1.5 \times 10^{5} J$ . The pressure of Helium in the cylinder is

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$2 \times 10^{6} N / m^{2}$

$3 \times 10^{6} N / m^{2}$

$4 \times 10^{6} N / m^{2}$

$5 \times 10^{6} N / m^{2}$

answer is D.

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Detailed Solution

$Kinetic energy E = 1.5 \times 10^{5} J,$

$volume V = 20 litre = 20 \times 10^{- 3} m^{3}$

$Pressure = \frac{2}{3} \frac{E}{V}$

$= \frac{2}{3} (\frac{1.5 \times 10^{5}}{20 \times 10^{- 3}}) = 5 \times 10^{6} N / m^{2} .$

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