The ideal gas equation is $pV=\frac{1}{3}Nm<c^2>$. State the meaning of the symbols $\mathrm{Nm}$ and $<c^2>$.

The ideal gas equation is $pV=\frac{1}{3}Nm<c^2>$. A cylinder of helium-4 contains gas with volume $4.1\times {10}^4{ \mathrm{cm}}^3$ at a pressure of $6.0\times {10}^5 \mathrm{Pa}$ and a temperature of $22°\mathrm{C}$. You may assume helium acts as an ideal gas and that a molecule of helium-4 contains 4 nucleons, each of mass $1.66\times {10}^{-27} \mathrm{kg}$. Determine the amount of gas in mole

The ideal gas equation is $pV=\frac{1}{3}Nm<c^2>$. A cylinder of helium-4 contains gas with volume $4.1\times {10}^4{ \mathrm{cm}}^3$ at a pressure of $6.0\times {10}^5 \mathrm{Pa}$ and a temperature of $22°\mathrm{C}$. You may assume helium acts as an ideal gas and that a molecule of helium-4 contains 4 nucleons, each of mass $1.66\times {10}^{-27} \mathrm{kg}$. Determine the number of molecules present in the gas.

The ideal gas equation is $pV=\frac{1}{3}Nm<c^2>$. A cylinder of helium-4 contains gas with volume $4.1\times {10}^4{ \mathrm{cm}}^3$ at a pressure of $6.0\times {10}^5 \mathrm{Pa}$ and a temperature of $22°\mathrm{C}$. You may assume helium acts as an ideal gas and that a molecule of helium-4 contains 4 nucleons, each of mass $1.66\times {10}^{-27} \mathrm{kg}$. Determine the root-mean-square speed of the molecules.

State what is meant by an ideal gas.

(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.