Pressure vs Velocity

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. $2\times {10}^{6}N/m^2$

2. $3\times {10}^{6}N/m^2$

3. $4\times {10}^{6}N/m^2$

4. $5\times {10}^{6}N/m^2$

Q.

The relation between the gas pressure P and average kinetic energy per unit volume E is

1. $P=\frac{1}{2}E$

2. $P=E$

3. $P=\frac{3}{2}E$

4. $P=\frac{2}{3}E$

Q.

The water tank on the roof of a building has its water level at a height of $10m$ above a water tap on the ground floor. Calculate,

1. The hydrostatic pressure at the water tap,
2. Total pressure at a point inside the pipe at the level of the tap, and
3. The pressure with which rushes out of the tap.

Take atmospheric pressure = ${10}^{5}Pa$.

Q.

The relation between the gas pressure P and average kinetic energy per unit volume E is

1. $P=\frac{1}{2}E$

2. $P=E$

3. $P=\frac{3}{2}E$

4. $P=\frac{2}{3}E$

Q.

What is meant by the statement ‘the atmospheric pressure at a place is ’76 cm of Hg? State its value in Pa.

Q. The graph shows hypothetical speed distribution for a sample of 𝑁 gas particles (for $V_0,\frac{dN}{dV}=0$)

1. The value of $a{V}_0$ is $2N$
2. The ratio $\frac{V_{avg}}{V_0}$ is equal to $\frac{2}{3}$
3. The ratio $\frac{V_{rms}}{V_0}$ is equal to $\frac{1}{\sqrt{2}}$
4. Three-fourths of the total particles have a speed between $0.5V_0$ and $V_0$

Q.

Pressure is exerted by a gas on the walls of the container because

1. It loses kinetic energy

2. It sticks with the walls

3. On collision with the walls there is a change in momentum

4. It is accelerated towards the walls

Q.

Assume that the temperature remains essentially constant in the upper part of the atmosphere. Obtain an expression for the variation in pressure with height in the upper atmosphere. The mean molecular weight of air is M. Assume a variable $P_O$ for the pressure at a height h = 0, where h = 0 depends on the choice of origin (could very well be at the beginning of the stratosphere, for example).

1. $P=P_0{e}^{-\frac{Mgh}{RT}}$

2. $P=P_0{e}^{-\frac{RT}{Mgh}}$

3. $P=P_0{e}^{\frac{Mgh}{RT}}$

4. $P=P_0{e}^{\frac{RT}{Mgh}}$.

Q.

Figure shows a vertical cylindrical vessel separated in two parts by a frictionless piston free to move along the length of the vessel. The length of the cylinder is 90 cm and the piston divides the cylinder in the ratio of 5:4. Each of the two parts of the vessel contains 0.1 mole of an ideal gas. The temperature of the gas is 300 K in each part. Calculate the mass of the piston

1. 10.3 kg

2. 5.7 kg

3. 12.7 kg

4. 15.5 kg

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. 68.45 cms Hg

2. 72.00 cms Hg

3. 75.39 cms Hg

4. 82.21 cms Hg

Q.

${10}^{23}$ molecules of nitrogen, argon and carbon dioxide each are confined in three closed boxes of a large fixed volume V, at the same temperature T. Knowing the molecular weights of the gases are in the order $M_{C{O}_2}$>$M_{N_2}$>$M_{A_r}$, what can you say about the pressures of the gases in each container?

1. $P_{A_r}$ > $P_{N_2}$ > $P_{C{O}_2}$

2. $P_{C{O}_2}$ > $P_{N_2}=P_{A_r}$

3. $P_{C{O}_2}$ > $P_{N_2}$ > $P_{C{O}_2}$

4. $P_{A_r}=P_{N_2}=P_{C{O}_2}$

Q.

A rigid cubical box of volume $1c{m}^3$ filled with 1 mol of Helium at high pressure, is slowly cooled to 0 K, in your school laboratory. What will be the pressure on the bottom wall? Assume no interactions between the atoms other than elastic collisions

1. 0 Pa
2. 400 Pa
3. It will not be a constant value
4. 8.2 Pa

Q.

A beam of hydrogen molecules is directed toward a wall, at an angle ${32}^{\circ }$ with the normal to the wall. Each molecule in the beam has a speed of 1.0 km/s and a mass of $3.3\times {10}^{24}g$. The beam strikes the wall over an area of $2.0C{m}^2$, at a rate of $4.0\times {10}^{23}$ molecules per second. What is the beam's pressure on the wall?

1. 11 kPa

2. 1 kPa

3. 9 kPa

4. 13 kPa

Q.

A rigid cubical box of volume $1c{m}^3$ filled with 1 mol of Helium at high pressure, is slowly cooled to 0 K, in your school laboratory. What will be the pressure on the bottom wall? Assume no interactions between the atoms other than elastic collisions

1. 0 Pa
2. 400 Pa
3. It will not be a constant value
4. 8.2 Pa

Q. Try to derive the relationship between pressure and the sum of velocities (say, v) of each molecule, density of the gas ($\rho$), and the total number of particles in the container (N).

1. $\frac{1}{3}\rho \Sigma \frac{v^2}{N}$
2. $\frac{1}{2}\rho \Sigma \frac{v^2}{N}$
3. $\frac{1}{4}\rho \Sigma \frac{v^2}{N}$
4. Common man, I don't wanna do this.

Q. Each molecule of mass $m$ of a monoatomic gas has got three degrees of freedom. The r.m.s. velocity of these molecules 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. $\sqrt{\frac{5}{3}}v$
2. $\sqrt{\frac{3}{5}}v$
3. $v$
4. None of these

Q.

If the mean free path of atoms is doubled then the pressure (P) of gas will become

1. $\frac{P}{4}$

2. $\frac{p}{2}$

3. $\frac{p}{8}$

4. P

Q.

A beam of hydrogen molecules is directed toward a wall, at an angle ${32}^{\circ }$ with the normal to the wall. Each molecule in the beam has a speed of 1.0 km/s and a mass of $3.3\times {10}^{24}g$. The beam strikes the wall over an area of $2.0C{m}^2$, at a rate of $4.0\times {10}^{23}$ molecules per second. What is the beam's pressure on the wall?

1. 11 kPa

2. 1 kPa

3. 9 kPa

4. 13 kPa