Ideal Gas Laws

Correct gas equation is:

$600 \mathrm{c}.\mathrm{c}.$ of a gas at a pressure of $750 \mathrm{mm}$ is compressed to $500 \mathrm{c}.\mathrm{c}$. Taking the temperature to remain constant, the increase in pressure, is

The ratio amongst most probable velocity, mean velocity and root mean square velocity is given by

Under what conditions will a pure sample of an ideal gas not only exhibit a pressure of $1 \mathrm{atm}$ but also a concentration of $1 \mathrm{mole} {\mathrm{L}}^{-1}$?

$(\mathrm{R}=0.082 \mathrm{L}\mathrm{atm}{\mathrm{mol}}^{-1}{\mathrm{deg}}^{-1})$

Select one correct statement. In the gas equation, PV = nRT

A closed flask contains water in all its three states, solid, liquid and vapour at $\mathrm{}\mathrm{}\mathrm{}\mathrm{}0°C$ . In this situation, the average kinetic energy of water molecules will be

If $P,V,M, T \mathrm{and} R$ are pressure, volume, molar mass, temperature and gas constant respectively, then for an ideal gas, the density is given by

At what temperature the root-mean-square speed of nitrogen at $27 °\mathrm{C}$ would be tripled?

From the kinetic theory of gas, prove that $P=\frac{1}{3}{\rho \overline{c}}^2,$ where $\rho$ is the density of the gas and $\overline{c}$ is the root mean square velocity of the gas molecules. Show that $\overline{c}\propto \sqrt{T}$, where $T$ is the absolute temperature.

The saturated water vapour pressure on a planet is, $p_0=760 \mathrm{mm} \mathrm{Hg}$. Determine the vapour density $\rho$.

A closed vessel contains a mixture of two diatomic gases $A$ and $B$. Molar mass of $A$ is $16$ times that of '$B$' and mass of gas $A$ is $2$ times that of '$B$'. ThenNumber of molecules of gas $B$ in the vessel is eight times that of $A$

In the cylinder shown in the figure, air is enclosed under the piston. Piston mass $M=60 \mathrm{kg},$ cross sectional area of the cylinder $S_0=20{ \mathrm{cm}}^2,$ atmospheric pressure $P_0={10}^5 Pa,\mathrm{\alpha }=37°.$ The air temperature is constant, the friction is negligible.

Choose the correct statement(s):

In a cylindrical container of sufficiently large height, two easily moving pistons enclose certain amount of same ideal gas in two chambers as shown in the figure.

The upper piston is at a height $20 \mathrm{cm}$ from the bottom and lower piston is at a height $8 \mathrm{cm}$from the bottom. The mass of each piston is $m\mathrm{kg}$ and cross sectional area of each piston is $A{m}^2,$ where $\frac{mg}{A}=P_0$ and $P_0$ is the atmospheric pressure $=1\times {10}^5 \mathrm{N} {\mathrm{m}}^{-2}.$

The cylindrical container and pistons are made of conducting material. Initially the temperature of gas is $27°\mathrm{C}$ and whole system is in equilibrium. Now if the upper piston is slowly lifted by $16 \mathrm{cm}$ and held in that position with the help of some external force. As a result, the lower piston rises slowly by $\mathrm{cm}.$

According to Maxwell's distribution of molecular speeds for the below graph for two different samples of ideal gases $A$ and $B$ at temperature $T_1$ and $T_2$ respectively which of the following statements is/are INCORRECT

The pressure of an ideal gas of $\text{'}n\text{'}$ moles whose pressure $P$ is related to its volume $V$ as $P=P_0{e}^{-\alpha V}$ $(P_0$ and $\alpha$ are positive constants of appropriate dimensions). The maximum attainable temperature of this ideal gas is $\frac{k{P}_0}{\left(ne\alpha R\right)},$ when it's volume $V=\frac{j}{\alpha };$ The value of $(j, k)$ are

Consider the shown diagram where the two chambers separated by pistonspring arrangement contain equal amounts of certain ideal gas. Initially when the temperatures of the gas in both the chambers are kept at $300 K\mathit{,}$ the compression in the spring is $1 m.$ The temperature of the left and the right chambers are now raised to $400 K$ and $500 K$ respectively. If the pistons are free to slide, the final compression in the spring (in $m$ ) is

On the basis of the kinetic theory of gases if we compare $1$ gram of hydrogen with $1$ gram of argon. Then,

One mole of an ideal monoatomic gas (initial temperature $T_0)$ is made to go through the cycle abca shown figure. If $U$ denotes the internal energy, then choose the correct statement(s). $(\text{'}ca\text{'}$ is a curve)

When an excited $\mathrm{H}$ atom goes to ground state it emits a photon.

Statement 1 : Mass has changed into energy.
Statement 2 : K.E. has increased.