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A cylinder of capacity 20 litres is filled with $H_{2}$ gas. The total average kinetic energy of translatory motion of its molecules is $1 .5 \times 10^{5} J$ . The pressure of hydrogen 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

$V = 20 litres = 20 (1000) c c = 20 \times 10^{- 3} m^{3}$

$KE = \frac{3}{2} (nRT) = 1 .5 \times 10^{5} J$

$\Rightarrow nRT = 10^{5} . . . . . . (1)$

From ideal gas equation

$PV = nRT \Rightarrow PV = (10^{5})$

$\Rightarrow P (20 \times 10^{- 3}) = (1) (10^{5})$

$\Rightarrow P (20 \times 10^{- 3}) = (1) (10^{5}) \Rightarrow P = 5 \times 10^{6} {Nm}^{- 2}$

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