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In a certain region of space there are only $5$ gaseous molecules per $c m^{3}$ on an average. The temperature there is $3 K$ . The pressure of this gas is $(k_{B} = 1.38 x 10^{- 23} J m o l^{- 1} K^{- 1})$

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$10.7 x 10^{- 16} N m^{- 2}$

$20.7 x 10^{- 17} N m^{- 2}$

$10.7 x 10^{- 17} N m^{- 2}$

$20.7 x 10^{- 16} N m^{- 2}$

answer is B.

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Detailed Solution

Let $n$ be the number of molecules in the gas

$P V = n k_{B} T$ or $P = \frac{n k_{B} T}{V}$

Here, $\frac{n}{V} = 5 c m^{- 3} = 5 x 10^{6} m^{- 3}$

$k_{B} = 1.38 x 10^{- 23} J m o l^{- 1} K^{- 1} P = 5 x 10^{6} x 1.38 x 10^{- 23} x 3 = 20.7 x 10^{- 17} N m^{- 2}$

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