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Q.

A cylinder of capacity 20 litre 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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a

$2 \times 10^{6} {Nm}^{- 2}$

b

$3 x 10^{6} {Nm}^{- 2}$

c

$4 \times 10^{6} {Nm}^{- 2}$

d

$5 \times 10^{6} {Nm}^{- 2}$

answer is D.

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Detailed Solution

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$\begin{array}{l} V = 20 litre = 20 (1000) cc = 20 \times 10^{- 3} m^{3} \\ average K . E = \frac{3}{2} ({NK}_{B} T) = 1 .5 \times 10^{5} J \\ \Rightarrow T = \frac{10^{5}}{{Nk}_{B}} \\ (or) RT = N_{A} (10^{5}) \dots (1) \end{array}$
From ideal gas equation
$\begin{array}{l} PV = nRT = (\frac{N}{N_{A}} | RT \dots (2) | \\ PV = {Nk}_{B} T \\ PV = {Nk}_{B} \frac{10^{5}}{{Nk}_{B}} \\ \Rightarrow P \times 20 \times 10^{- 3} = 10^{5} \Rightarrow P = 5 \times 10^{6} {Nm}^{- 2} \end{array}$

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