Question

Two kg of a monoatomic gas is at a pressure of $4\times {10}^{4}N/m^2$ . The density of the gas is $8kg/m^3$. What is the order of energy of the gas due to its thermal motion ?

• A. ${10}^{3}J$
• B. ${10}^{5}J$
• C. ${10}^{6}J$
• D. ${10}^{4}J$

Answer 1

The correct option is D ${10}^{4}J$

Thermal energy of N molecule
$=N\left(\frac{3}{2}kT\right)$
$=\frac{N}{N_A}\frac{3}{2}RT$
$=\frac{3}{2}\left(nRT\right)$
$=\frac{3}{2}PV$
$=\frac{3}{2}P\left(\frac{m}{8}\right)$
$=\frac{3}{2}\times 4\times {10}^4\times \frac{2}{8}$
$=1.5\times {10}^4$
order will ${10}^4$.