(b) A cylinder contains $500 \mathrm{g}$ of helium-4 at a pressure of $5.0\times {10}^5 \mathrm{Pa}$ and at a temperature of $27°\mathrm{C}$. You may assume that the molar mass of helium- 4 is $4.0 \mathrm{g}$. Calculate:

(i) The number of moles of helium the cylinder hold.

(b) A cylinder contains $500 \mathrm{g}$ of helium-4 at a pressure of $5.0\times {10}^5 \mathrm{Pa}$ and at a temperature of $27°\mathrm{C}$. You may assume that the molar mass of helium- 4 is $4.0 \mathrm{g}$. Calculate:

(ii) the number of atoms of helium the cylinder holds.

A cylinder contains $500 \mathrm{g}$ of helium-4 at a pressure of $5.0\times {10}^5 \mathrm{Pa}$ and at a temperature of $27°\mathrm{C}$. You may assume that the molar mass of helium- 4 is $4.0 \mathrm{g}$. Calculate the volume of the cylinder.

One assumption of the kinetic theory of gases is that molecules undergo perfectly elastic collisions with the walls of their container. Explain what is meant by a perfectly elastic collision.

One assumption of the kinetic theory of gases is that molecules undergo perfectly elastic collisions with the walls of their container. State three other assumptions of the kinetic theory.

A single molecule is contained within a cubical box of side length $0.30 \mathrm{m}$. The molecule, of mass $2.4\times {10}^{-26} \mathrm{kg}$, moves backwards and forwards parallel to one side of the box with a speed of $400 \mathrm{m}{ \mathrm{s}}^{-1}$. It collides elastically with one of the faces of the box, face $\mathrm{P}$. Calculate the change in momentum each time the molecule hits face $\mathrm{P}$.

A single molecule is contained within a cubical box of side length $0.30 \mathrm{m}$. The molecule, of mass $2.4\times {10}^{-26} \mathrm{kg}$, moves backwards and forwards parallel to one side of the box with a speed of $400 \mathrm{m}{ \mathrm{s}}^{-1}$. It collides elastically with one of the faces of the box, face $\mathrm{P}$. Calculate the number of collisions made by the molecule in $1.0 \mathrm{s}$ with face $\mathrm{P}$.

A single molecule is contained within a cubical box of side length $0.30 \mathrm{m}$. The molecule, of mass $2.4\times {10}^{-26} \mathrm{kg}$, moves backwards and forwards parallel to one side of the box with a speed of $400 \mathrm{m}{ \mathrm{s}}^{-1}$. It collides elastically with one of the faces of the box, face $\mathrm{P}$. Calculate the mean force exerted by the molecule on face $\mathrm{P}$.

A cylinder contains $1.0 \mathrm{mol}$ of an ideal gas. The gas is heated while the volume of the cylinder remains constant. Calculate the energy required to raise the temperature of the gas by $1.0°\mathrm{C}$.