At $300\,K$, the rms speed of oxygen molecules is $\sqrt{\frac{\alpha+5}{\alpha}}$ times to that of its average speed in the gas. Then, the value of $\alpha$ will be (used $\pi=\frac{22}{7}$ )
A$32$
B$28$
C$24$
D$27$
JEE MAIN 2023, Medium
Download our app for free and get started
B$28$
b $\sqrt{\frac{3 RT }{ M }}=\sqrt{\frac{\alpha+5}{\alpha}} \sqrt{\frac{8}{\pi} \frac{ RT }{ M }}$
$3=\frac{\alpha+5}{\alpha} \frac{8}{\pi}$
$\alpha=28$
Download our app
and get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
A cylindrical container of volume $4.0 \times 10^{-3} \,{m}^{3}$ contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is $400 \,{K}$ The pressure of the mixture of gases is:
[Take gas constant as $8.3\, {J} {mol}^{-1} {K}^{-1}$]
A gas at absolute temperature $300\,K$ has pressure $= 4 \times 10^{-10}\,N /m^2$ . Boltzmann constant, $k = 1.38 \times 10^{-23}\,J / K$ . The number of molecules per $cm^3$ is of the order of
Molar specific heat of oxygen at constant pressure ${C_p} = 7.2\,cal/mol^\circ C$ and $R = 8.3 joule/mol/K$. At constant volume, $5\, mol$ of oxygen is heated from $10°C$ to $20°C$, the quantity of heat required is approximately ........ $cal$
The root mean square speed of molecules of nitrogen gas at $27^{\circ} C$ is approximately$.......m/s$(Given mass of a nitrogen molecule $=4.6 \times 10^{-26}\,kg$ and take Boltzmann constant $k _{ B }=1.4 \times 10^{-23}\,JK ^{-1}$ )
An ideal gas is enclosed in a cylinder at pressure of $2\,atm$ and temperature, $300\,K.$ The mean time between two successive collisions is $6 \times 10^{-8}\, s.$ If the pressure is doubled and temperature is increased to $500\,K,$ the mean time between two successive collisions will be close to
The root mean square speed of hydrogen molecules of an ideal hydrogen gas kept in a gas chamber at $0°C$ is $3180$ metres/second. The pressure on the hydrogen gas is ..... $atm$ (Density of hydrogen gas is $8.99 \times {10^{ - 2}}\,kg/{m^3}$, $1$ atmosphere $ = 1.01 \times {10^5}\,N/{m^2})$