Question

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?
$(k_B=1.38\times {10}^{-23}$J $mo{l}^{-1}$ $K^{-1}$)

• A. $20.7\times {10}^{-16}$N $m^{-2}$
• B. $20.7\times {10}^{-17}$N $m^{-2}$
• C. $10.7\times {10}^{-16}$N $m^{-2}$
• D. $10.7\times {10}^{-17}$N $m^{-2}$

Answer 1

The correct option is B $20.7\times {10}^{-17}$N $m^{-2}$

Let n be the number of molecules in the gas PV$=n{K}_{B}T$
or $P=\frac{n{K}_{B}T}{V}$
Here, $\frac{n}{V}=5c{m}^{-3}=5\times {10}^6{m}^{-3}$
$k_B=1.38\times {10}^{-23}$J $mo{l}^{-1}{K}^{-1}$
$\therefore P=5\times {10}^6\times 1.38\times {10}^{-23}\times 3$
$=20.7\times {10}^{-17}$N $m^{-2}$