Question

A vessel contains $6\times {10}^{29}$ molecules of a gas per cubic metre. The mass of each molecule is $5\times {10}^{-27}$ kg. If the molecules are moving with velocity 1 Km $se{c}^{-1}$.What is the pressure of the gas?

• A. ${10}^3$ Pa
• B. ${10}^5$ Pa
• C. ${10}^7$ Pa
• D. ${10}^9$ Pa

Answer 1

Answer: (D)

${10}^9$ Pa

Applying formula, $PV=1/3mN{v}^2$

or, $P=1/3m\left(N/V\right)v^2$

where P is pressure

m is mass of molecule.

(N/V) is number of molecules per unit volume.

v is velocity of molecule.

$m$ = $5\times {10}^{-27}$ Kg,

$N/V=6\times {10}^{29}/m^3$

$v=1km/sec=1000m/s$

now, Pressure, $P=1/3\times 5\times {10}^{-27}kg\times (6\times {10}^{29}/m^3)\times (1000m/s{)}^2$

$=5\times {10}^2\times 2\times {10}^{6}Kg/m/s^2$

$=10\times {10}^{8}N/m^2$

$={10}^{9}N/m^2$

Hence, the pressure of a gas in the vessel is ${10}^9$ Pa.