A cubic vessel (with face horizontal + vertical) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a speed of $500 \mathrm{~m} \mathrm{~s}^{-1}$ in vertical direction. The pressure of the gas inside the vessel as observed by us on the ground

1 mole of an ideal gas is contained in a cubical volume $V, A B C D E F G H$ at 300 K (figure). One face of the cube ( $E F G H$ ) is made up of a material which totally absorbs any gas molecule incident on it. At any given time,

Boyle's law is applicable for an

A cylinder containing an ideal gas is in vertical position and has a piston of mass $M$ that is able to move up or down without friction (figure). If the temperature is increased

Volume versus temperature graphs for a given mass of an ideal gas are shown in figure. At two different values of constant pressure. What can be inferred about relation between $p_1$ and $p_2$ ?

1 mole of $\mathrm{H}_2$ gas is contained in a box of volume $V=1.00 \mathrm{~m}^3$ at $T=300 \mathrm{~K}$. The gas is heated to a temperature of $T=3000 \mathrm{~K}$ and the gas gets converted to a gas of hydrogen atoms. The final pressure would be (considering all gases to be ideal)

A vessel of volume $V$ contains a mixture of 1 mole of hydrogen and 1 mole oxygen (both considered as ideal). Let $f_1(v) d v$, denote the fraction of molecules with speed between $v$ and $(v+d v)$ with $f_2(v) d v$, similarly for oxygen. Then,

An inflated rubber balloon contains one mole of an ideal gas, has a pressure $p$, volume $V$ and temperature $T$. If the temperature rises to 1.1 T , and the volume is increased to 1.05 V , the final pressure will be

$A B C D E F G H$ is a hollow cube made of an insulator (figure) face $A B C D$ has positive charge on it. Inside the cube, we have ionised hydrogen. The usual kinetic theory expression for pressure

Diatomic molecules like hydrogen have energies due to both translational as well as rotational motion. From the equation in kinetic theory $p V=\frac{2}{3} E, E$ is

In a diatomic molecule, the rotational energy at a given temperature

Which of the following diagrams (figure) depicts ideal gas behaviour?

When an ideal gas is compressed adiabatically, its temperature rises the molecules on the average have more kinetic energy than before. The kinetic energy increases,

Calculate the number of atoms in 39.4 g gold. Molar mass of gold is $197 \mathrm{~g} \mathrm{~mole}^{-1}$.

The volume of a given mass of a gas at $27^{\circ} \mathrm{C}, 1 \mathrm{~atm}$ is 100 cc . What will be its volume at $327^{\circ} \mathrm{C}$ ?

The molecules of a given mass of a gas have root mean square speeds of $100 \mathrm{~ms}^{-1}$ at $27^{\circ} \mathrm{C}$ and 1.00 atmospheric pressure. What will be the root mean square speeds of the molecules of the gas at $127^{\circ} \mathrm{C}$ and 2.0 atmospheric pressure?

Two molecules of a gas have speeds of $9 \times 10^6 \mathrm{~ms}^{-1}$ and $1 \times 10^6 \mathrm{~ms}^{-1}$, respectively. What is the root mean square speed of these molecules.

A gas mixture consists of 2.0 moles of oxygen and 4.0 moles of neon at temperature $T$. Neglecting all vibrational modes, calculate the total internal energy of the system. (0xygen has two rotational modes.)

Calculate the ratio of the mean free paths of the molecules of two gases having molecular diameters 1$$\mathop A\limits^o $$ and 2$$\mathop A\limits^o $$. The gases may be considered under identical conditions of temperature, pressure and volume.

The container shown in figure has two chambers, separated by a partition, of volumes $V_1=2.0 \mathrm{~L}$ and $V_2=3.0 \mathrm{~L}$. The chambers contain $\mu_1=4.0$ and $\mu_2=5.0$ mole of a gas at pressures $p_1=1.00 \mathrm{~atm}$ and $p_2=2.00 \mathrm{~atm}$. Calculate the pressure after the partition is removed and the mixture attains equilibrium.

A gas mixture consists of molecules of $A, B$ and $C$ with masses $m_A>m_B>m_C$. Rank the three types of molecules in decreasing order of (a) average KE (b) rms speeds.

We have 0.5 g of hydrogen gas in a cubic chamber of size 3 cm kept at NTP. The gas in the chamber is compressed keeping the temperature constant till a final pressure of 100 atm . Is one justified in assuming the ideal gas law, in the final state? (Hydrogen molecules can be consider as spheres of radius $1 \mathop A\limits^o$ ).

When air is pumped into a cycle tyre the volume and pressure of the air in the tyre both are increased. What about Boyle's law in this case?

A balloon has 5.0 mole of helium at $7^{\circ} \mathrm{C}$. Calculate

(a) the number of atoms of helium in the balloon.

(b) the total internal energy of the system.

Calculate the number of degrees of freedom of molecules of hydrogen in 1 cc of hydrogen gas at NTP.

An insulated container containing monoatomic gas of molar mass $m$ is moving with a velocity $v_0$. If the container is suddenly stopped, find the change in temperature.

Explain why

(a) there is no atmosphere on moon

(b) there is fall in temperature with altitude

Consider an ideal gas with following distribution of speeds.

(a) Calculate $v_{\text {rms }}$ and hence $T .\left(m=3.0 \times 10^{-26} \mathrm{~kg}\right)$

(b) If all the molecules with speed $1000 \mathrm{~m} / \mathrm{s}$ escape from the system, calculate new $v_{\text {rms }}$ and hence $T$.

Ten small planes are flying at a speed of $150 \mathrm{~km} / \mathrm{h}$ in total darkness in an air space that is $20 \times 20 \times 1.5 \mathrm{~km}^3$ in volume. You are in one of the planes, flying at random within this space with no way of knowing where the other planes are. On the average about how long a time will elapse between near collision with your plane. Assume for this rough computation that a saftey region around the plane can be approximated by a sphere of radius 10 m .

A box of $1.00 \mathrm{~m}^3$ is filled with nitrogen at 1.50 atm at 300 K . The box has a hole of an area $0.010 \mathrm{~mm}^2$. How much time is required for the pressure to reduce by 0.10 atm, if the pressure outside is 1 atm .

Consider a rectangular block of wood moving with a velocity $v_0$ in a gas at temperature $T$ and mass density $\rho$. Assume the velocity is along $x$-axis and the area of cross-section of the block perpendicular to $v_0$ is $A$. Show that the drag force on the block is $4 r A v_0 \sqrt{\frac{k T}{m}}$, where, $m$ is the mass of the gas molecule.