Pressure vs Velocity

Q. If $15\text{g}$ mass of nitrogen gas is enclosed in a vessel at a temperature ${27}^{\circ }\text{C}$. Amount of heat transfered to the gas, so that rms velocity of molecules is doubled is about
[Take $R=8.3\text{J/K mole}$]

1. $\text{14 kJ}$
2. $\text{6 kJ}$
3. $\text{0.9 kJ}$
4. $\text{10 kJ}$

Q. The mass of hydrogen molecule is $3.32\times {10}^{-27}\text{kg}$. If ${10}^{23}$ hydrogen molecules strike per second at $2{\text{cm}}^2$ area of rigid wall of a close container normally and rebound back with the speed of $1000\text{m/s}$, then the pressure exerted on the wall (according to kinetic theory of gas) is

1. $3000{\text{N/m}}^2$
2. $6640{\text{N/m}}^2$
3. $8320{\text{N/m}}^2$
4. $3320{\text{N/m}}^2$

Q.

The root mean square speed of molecules of a given mass of a gas at 27⁰C and 1 atmosphere pressure is 200 ms^-1. The root mean square speed of molecules of the gas at 127⁰C and 2 atmosphere pressure is x/√3 ms^-1. The value of x will be __________.

Q. An ideal gas has molar heat capacity at constant pressure $C_p=\frac{5R}{2}$. The gas is kept in a cylindrical vessel fitted with a piston which is free to move. Mass of the frictionless piston is 9 kg. Initial volume of the gas is $0.0027m^3$ and cross-section area of the piston is $0.09m^2$. The initial temperature of the gas is 300 K. Atmospheric pressure $P_0=1.05\times {10}^{5}N/m^2$. An amount of $2.5\times {10}^{4}J$ of heat energy is supplied to the gas such that piston move without acceleration, then

1. Initial pressure of the gas is $1.06\times {10}^{5}N/m^2$
2. Work done by the gas is 1000 $J$
3. Final pressure of the gas is $1.06\times {10}^{5}N/m^2$
4. Work done by gas is $9.94\times {10}^{3}J$

Q. Hydrogen gas is filled in a balloon at ${20}^{\circ }C$. If temperature is made ${40}^{\circ }C$, pressure remaining same, what fraction of hydrogen will come out

1. 0.25
2. 0.5
3. 0.75
4. 0.07

Q. The temperature of a gas is raised while keeping its volume constant. The pressure exerted by the gas on the walls of the container increases because its molecules

1. lose more kinetic energy to the wall.
2. gain more kinetic energy from the wall.
3. strike the wall more often with higher velocities.
4. strike the wall less frequently with lower velocities.

Q.

A cylinder of capacity 20 litres is filled with $H_2$ gas. The total average kinetic energy of translatory motion of its molecules is $1.5\times {10}^{5}J$. The pressure of hydrogen in the cylinder is

1. 

2. 

3. 

4. 

Q. Gas molecules has RMS speed $200\text{m/s}$ at ${27}^{\circ }\text{C}$ and $1\text{atm}$ pressure. If the RMS speed changes to $\frac{x}{\sqrt{3}}\text{m/s}$ when temperature becomes ${127}^{\circ }\text{C}$ and pressure becomes $2\text{atm}$, then the value of $x$ is

1. $100$
2. $200$
3. $300$
4. $400$

Q. Each molecule of mass $m$ of a monoatomic gas has got three degrees of freedom. The r.m.s. velocity of these atoms is $v$ at temperature $T$. For a diatomic molecule of mass $m$ and temperature $T$ which has got five degrees of freedom, r.m.s. velocity of molecule is

1. $\sqrt{\frac{3}{5}}v$
2. $\sqrt{\frac{5}{3}}v$
3. None of these
4. $v$

Q. The macroscopic properties of gases include its pressure (P), volume (V), its temperature (T), the quantity of the gas, which can be measured by its mass (M), or the number of gas particles (atoms/molecules; N). One of the earliest investigations on a relationship between these properties was conducted by Robert Boyle, chiefly motivated by a hunch against one of his contemporary, Toricelli's claim on how a barometer works. Boyle's set-up was as shown.

He attached a small U-tube at the end of a Toricellian tube and powered in mercury from the open end (T); as mercury rose in the closed, shorter column, the trapped air would get more and move compressed - which could only mean, that the pressure increased, and the volume decreased (these were respectively measured by the height of the mercury column, h, and a scale on the shorter column, V, for volume of the trapped air).

Which of these statements is/are correct in regard to Boyle's conclusion from the data?

1. The height difference of the two levels is directly proportional to the pressure of the trapped air

2. As the value of h increased, V monotonically decreased

3. If we blow air through the open end of T, then h would be a bad measure for the pressure of the trapped air

4. The graph of h versus the reciprocal of V is a straight line

Q. Consider a mixture of gas molecules of type $A,B$ and $C$ having masses, $m_A<m_B<m_C$. The ratio of their root-mean-square speeds at normal temperature and pressure is :

1. $v_A=v_B\ne v_C$
2. $\frac{1}{v_A}<\frac{1}{v_B}<\frac{1}{v_C}$
3. $\frac{1}{v_A}>\frac{1}{v_B}>\frac{1}{v_C}$
4. $v_A=v_B=v_C=0$

Q. The density of an ideal gas is $6\times {10}^{-2}{\text{kg/m}}^3$ and the root mean square velocity of the gas molecules is $500\text{m/s}$. The pressure exerted by the gas on the walls of the vessel is

1. $5\times {10}^3{\text{N/m}}^2$
2. $1.2\times {10}^{-4}{\text{N/m}}^2$
3. $0.75\times {10}^{-4}{\text{N/m}}^2$
4. $40{\text{N/m}}^2$

Q.

A thin tube of uniform cross section is sealed at both ends. It lies horizontally, the middle 5 cm containing mercury and the parts on its two sides containing air at the same pressure P. When the tube is held at an angle of ${60}^{\circ }$ with the vertical, the length of the air column above and below the mercury pellet are 46cm and 44.5cm respectively. Calculate the pressure P in centimeters of mercury. The temperature of the system is kept at ${30}^{\circ }C$.

1. 72.00 cms Hg

2. 75.39 cms Hg

3. 82.21 cms Hg

4. 68.45 cms Hg

Q. The molecules of a given mass of gas has r.m.s speed $400\text{m/s}$ at ${27}^{\circ }\text{C}$ and ${10}^5{\text{N/m}}^2$ pressure . When the absolute temperature is doubled and the pressure is halved, the r.m.s. speed of the molecules of the same gas is

1. $400\text{m/s}$
2. $200\sqrt{2}\text{m/s}$
3. $400\sqrt{2}\text{m/s}$
4. $1200\text{m/s}$

Q.

The change in the magnitude of the volume of an ideal gas when a small additional pressure $∆\mathrm{P}$ is applied at a constant temperature is the same as the change when the temperature is reduced by a small quantity $∆\mathrm{T}$at constant pressure. The initial temperature and pressure of the gas were $300\mathrm{K}$ and$2\mathrm{atm}$. respectively. If $\left|∆\mathrm{T}\right|=\mathrm{C}\left|∆\mathrm{P}\right|$then the value of C in ($\mathrm{K}{\mathrm{atm}}^{-1}$) is __________.

Q. The speed of a molecule of gas in a cubical vessel of side $4\text{m}$ is $16\text{m/s}$. This molecule is constantly colliding with the wall of the container. The collision frequency will be

1. $2{\text{s}}^{-1}$
2. $4{\text{s}}^{-1}$
3. $6{\text{s}}^{-1}$
4. $1{\text{s}}^{-1}$

Q. The temperature of a gas is raised while its volume remains constant, the pressure exerted by a gas on the walls of the container increases because its molecules

1. Collide with each other less frequency
2. Lose more kinetic energy to the wall
3. Are in contact with the wall for a shorter time
4. Strike the wall more often with higher velocities

Q. Two containers $A\text{and}B$ contain ideal gases, helium and oxygen respectively. Volume of both containers are equal, and pressure is also equal. Container $A$ has twice the number of molecules than container $B.$ If $V_A\text{and}{V}_B$ represent the rms speed of gases in containers $A\text{and}B$ respectively, then

1. $\frac{V_A}{V_B}=\sqrt{2}$
2. $\frac{V_A}{V_B}=4$
3. $\frac{V_A}{V_B}=2$
4. $\frac{V_A}{V_B}=\sqrt{8}$

Q. The average translational kinetic energy of molecules of an ideal gas is (symbols have their usual meanings)

1. $\frac{1}{2}{k}_{B}T$
2. $\frac{3}{2}{k}_{B}T$
3. $\frac{7}{2}{k}_{B}T$
4. $\frac{5}{2}{k}_{B}T$

Q.

Molecules of a gas behave like

1. Inelastic rigid sphere

2. Perfectly elastic non-rigid sphere

3. Perfectly elastic rigid sphere

4. Inelastic non-rigid sphere

Q.

Have you ever wondered what the pressure is under the glass bell jar when the vacuum pump is turned on? One way to measure it would be to see how a balloon changes when it is inside. At beginning of the experiment, you note that the volume of the balloon is 560ml under standard pressure. When you turned on the vacuum pump the balloon grows to 780ml. What is the pressure under the bell jar at this point?

Q. A container has an ideal gas at pressure $P$ in thermal equilibrium. Assuming the mass of a molecule is $m$ and all the molecules are moving wih same speed $v$ in random directions, the expression for number of colloisions per second which the molecules make with unit area of container's wall is $\frac{\sqrt{xP}}{ymv}$. Find $(x+y)$

Q. The mass of a hydrogen molecule is $3.32\times {10}^{-27}\text{kg}$. If ${10}^{23}$ hydrogen molecules strike per second at $2{\text{cm}}^2$ area of rigid wall of a close container normally and rebound back with the speed of $1000\text{m/s}$, then the pressure exerted on the wall (according to kinetic theory of gas) is :

1. $3000{\text{N/m}}^2$
2. $6640{\text{N/m}}^2$
3. $8320{\text{N/m}}^2$
4. $3320{\text{N/m}}^2$

Q. An open cylindrical tube of cross-sectional area $A$ has two air tight frictionless pistons at its two ends. The pistons are tied with a straight piece of metallic wire. The tube contains a gas at atmospheric pressure $P_0$ and temperature $T_0$ in between the pistons. If temperature of the gas is doubled, then the tension in the wire is
(Assume that metallic wire is rigid)

1. $4P_{0}A$
2. $\frac{P_{0}A}{2}$
3. $P_{0}A$
4. $2P_{0}A$

Q.

Molecules of a gas behave like

1. Inelastic rigid sphere

2. Perfectly elastic non-rigid sphere

3. Perfectly elastic rigid sphere

4. Inelastic non-rigid sphere

Q. The energy of a gas per litre is 300 joules, then its pressure will be

1. 
2. 
3. 
4. 

Q. How this relation formed
surface energy/area=surface tension?
In byju's video they derived that surface energy =Surface tension .
Please explain I am confused .

Q.

A box contains n molecules of a gas. How will the pressure of the gas be effected, if the number of molecules is made 2n

1. Pressure will decrease

2. Pressure will remain unchanged

3. Pressure will be doubled

4. Pressure will become three times

Q. For a given gas at 1 atm pressure, rms speed of the molecules is 200 m/s at ${127}^{\circ }C.$ At 2 atm pressure and at ${227}^{\circ }C$, the rms speed of the molecules will be:

1. $100\sqrt{5}m/s$
2. $80m/s$
3. $80\sqrt{5}m/s$
4. $100m/s$

Q. Discuss the physical properties of a gas according to the postulates of kinetic theory of gases.