JEE Main - 4th April 2015

A vessel contains $14 \mathrm{g}$ of nitrogen gas at a temperature of $27°\mathrm{C}$. The amount of heat to be transferred to the gas to double the r.m.s. speed of its molecules will be : (Take $R=8.32 \mathrm{J} {\mathrm{mol}}^{-1}{\mathrm{k}}^{-1}$)

The root mean square speed of smoke particles of mass $5\times {10}^{-17} \mathrm{kg}$ in their Brownian motion in air at NTP is approximately.

[Given $k=1.38\times {10}^{-23}\mathrm{J} {\mathrm{K}}^{-1}$]

Given below are two statements:
Statement I: The temperature of a gas is $-73 °\mathrm{C}$. When the gas is heated to $527 °\mathrm{C}$, the root mean square speed of the molecules is doubled.
Statement II : The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules.
In the light of the above statements, choose the correct answer from the options given below:

The root mean square velocity of molecules of gas is

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 (use $\mathrm{\pi }=\frac{22}{7}$)

A flask contains hydrogen and oxygen in the ratio of $2 : 1$ by mass at temperature $27 °\mathrm{C}$. The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is :

The average kinetic energy of a molecule of the gas is

A bicycle tyre is filled with air having pressure of $270 \mathrm{kPa}$ at $27°\mathrm{C}$. The approximate pressure of the air in the tyre when the temperature increases to $36°\mathrm{C}$ is