Question

In a certain region of space there are only 5 gaseous molecules per cm3 on an average. The temperature there is 3 K. The pressure of this gas is (kB = 1.38 × 10–23 J mol–1 K–1)

• A. 20.7 × 10–16 N m–1
• B. 20.7 × 10–17 N m–1
• C. 10.7 × 10–16 N m–1
• D. 10.7 × 10–17 N m–1

Answer 1

Answer: (B)

20.7 × 10–17 N m–1

Answer 2

Let n be the number of molecules in the gas

$PV = nK_{B}T$or $P = \frac{nK_{B}T}{V}$

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

$k_{B} = 1.38 \times 10^{23}Jmol^{- 1}k^{- 1}$

$\therefore P = 5 \times 10^{- 6} \times 1.38 \times 10^{23} \times 3$

$= 20.7 \times 10^{- 17}Nm^{- 2}$