An ideal gas of N molecules is maintained at a constant pressure p. The graph shows how the volume V of the gas varies with absolute temperature T.

What is the gradient of the graph?

A. $\frac{N}{p}$

B. $\frac{NR}{p}$

C. $\frac{N{k}_{\mathrm{B}}}{p}$

D. $\frac{N}{Rp}$

Show that the initial quantity of potassium-40 in the rock sample was about 450 µmol.

An ideal gas is maintained at a temperature of 100 K. The variation of the pressure P and $\frac{1}{\text{volume}}$ of the gas is shown.

What is the quantity of the gas?

A.  $\frac{2\times {10}^5}{R} \text{mol}$

B.  $\frac{200}{R} \text{mol}$

C.  $\frac{80}{R} \text{mol}$

D.  $\frac{4}{5R} \text{mol}$

Explain, with reference to the kinetic model of an ideal gas, how an increase in temperature of the gas leads to an increase in pressure.

Cylinder X has a volume $V$ and contains 3.0 mol of an ideal gas. Cylinder Y has a volume $\frac{V}{2}$ and contains 2.0 mol of the same gas.

The gases in X and Y are at the same temperature $T$. The containers are joined by a valve which is opened so that the temperatures do not change.

What is the change in pressure in X?

A. $+\frac{1}{3}\left(\frac{RT}{V}\right)$

B. $-\frac{1}{3}\left(\frac{RT}{V}\right)$

C. $+\frac{2}{3}\left(\frac{RT}{V}\right)$

D. $-\frac{2}{3}\left(\frac{RT}{V}\right)$

Two flasks P and Q contain an ideal gas and are connected with a tube of negligible volume compared to that of the flasks. The volume of P is twice the volume of Q.

P is held at a temperature of 200 K and Q is held at a temperature of 400 K.

What is mass of $\frac{\mathrm{mass} \mathrm{of} \mathrm{gas} \mathrm{in} \mathrm{P}}{\mathrm{mass} \mathrm{of} \mathrm{gas} \mathrm{in} \mathrm{Q}}$?

A. $\frac{1}{8}$

B. $\frac{1}{4}$

C. 4

D. 8

State what is meant by an ideal gas.

The molar mass of an ideal gas is $M$. A fixed mass $m$ of the gas expands at a constant pressure $p$. The graph shows the variation with temperature T of the gas volume V.

What is the gradient of the graph?

A.  $\frac{Mp}{mR}$

B.  $\frac{MR}{mp}$

C.  $\frac{mp}{MR}$

D.  $\frac{mR}{Mp}$

A container holds 20 g of argon-40(${}_{18}^{40}\text{Ar}$)  and 40 g of neon-20 (${}_{10}^{20}\text{Ne}$) .

What is$\frac{\text{number of atoms of argon -40}}{\text{number of atoms of neon -20}}$ in the container?

A. 0.25

B. 0.5

C. 2

D. 4

Explain, using your answer to (d)(i) and with reference to the kinetic model, why this sample of helium can be assumed to be an ideal gas.

Calculate, in J, the internal energy of the gas.

Show that the number of helium atoms in the container is about 4 × 10²⁰.

Show that the number of helium atoms in the container is 4 × 10²⁰.

The door of the refrigerator has an area of 0.72 m². Show that the minimum force needed to open the refrigerator door is about 4 kN.

The molar mass of water is 18 g mol⁻¹. Estimate the average speed of the water molecules in the vapor produced. Assume the vapor behaves as an ideal gas.

Deduce whether helium behaves as an ideal gas over the temperature range 250 K to 500 K.

A fixed mass of an ideal gas has a volume of $V$, a pressure of p and a temperature of $30 °\text{C}$. The gas is compressed to the volume of $\frac{V}{6}$ and its pressure increases to 12p. What is the new temperature of the gas?

A.  $15 °\text{C}$

B.  $60 °\text{C}$

C.  $333 °\text{C}$

D.  $606 °\text{C}$

State what is meant by an ideal gas.

The temperature of the gas is increased to 500 K. Sketch, on the axes, a graph to show the variation with temperature T of the pressure P of the gas during this change.

Estimate the average speed of the helium atoms in the container.

Container X contains 1.0 mol of an ideal gas. Container Y contains 2.0 mol of the ideal gas. Y has four times the volume of X. The pressure in X is twice that in Y.

What is $\frac{\text{temperature of gas in X}}{\text{temperature of gas in Y}}$?

A.   $\frac{1}{4}$

B.   $\frac{1}{2}$

C.   1

D.   2

Calculate the average kinetic energy of the particles of the gas.

Discuss, by reference to the kinetic model of an ideal gas and the answer to (c)(i), whether the assumption that helium behaves as an ideal gas is justified.

The temperature of a fixed mass of an ideal gas changes from 200 °C to 400 °C.

What is $\frac{\text{mean kinetic energy of gas at 200 °C}}{\text{mean kinetic energy of gas at 400 °C}}$?

A. 0.50

B. 0.70

C. 1.4

D. 2.0

The student measured the height H of the air column and the corresponding air pressure p. After each reduction in the volume the student waited for some time before measuring the pressure. Outline why this was necessary.

Outline how the results of this experiment are consistent with the ideal gas law at constant temperature.

A gas storage tank of fixed volume V contains N molecules of an ideal gas at temperature T. The pressure at kelvin temperature T is 20 MPa. $\frac{N}{4}$ molecules are removed and the temperature changed to 2T. What is the new pressure of the gas?

A. 10 MPa

B. 15 MPa

C. 30 MPa

D. 40 MPa

A sealed container contains a mixture of oxygen and nitrogen gas.
The ratio $\frac{\text{mass of an oxygen molecule}}{\text{mass of a nitrogen molecule}}$ is $\frac{8}{7}$.

The ratio $\frac{\text{average kinetic energy of oxygen molecules}}{\text{average kinetic energy of nitrogen molecules}}$ is

A.  1.

B.  $\frac{7}{8}$.

C.  $\frac{8}{7}$.

D.  dependent on the concentration of each gas.

Calculate the pressure of the gas.

Calculate the number of atoms in the gas.

Calculate the volume of the oxygen produced in one second when it is allowed to expand to a pressure of 0.11 MPa and to reach a temperature of –13 °C.

Calculate the number of atoms in the gas.

With the door open the air in the refrigerator is initially at the same temperature and pressure as the air in the kitchen. Calculate the number of molecules of air in the refrigerator.

Explain, in terms of molecular motion, this change in pressure.

Calculate, in Pa, the new pressure of the gas.

Q and R are two rigid containers of volume 3V and V respectively containing molecules of the same ideal gas initially at the same temperature. The gas pressures in Q and R are p and 3p respectively. The containers are connected through a valve of negligible volume that is initially closed.

The valve is opened in such a way that the temperature of the gases does not change. What is the change of pressure in Q?

A.     +p

B.     $\frac{+p}{2}$

C.     $\frac{-p}{2}$

D.     –p

A solid cylinder of height h and density ρ rests on a flat surface.

Show that the pressure p_c exerted by the cylinder on the surface is given by p_c = ρgh.

Calculate the ratio $\frac{\text{volume of helium atoms}}{\text{volume of helium gas}}$.

Explain, with reference to the kinetic model of an ideal gas, how an increase in temperature of the gas leads to an increase in pressure.

Determine the pressure of the air inside the refrigerator.

Calculate the ratio  $\frac{\text{total volume of helium atoms}}{\text{volume of helium gas}}$.

The molar mass of helium is 4.0 g mol^-1. Show that the mass of a helium atom is 6.6 × 10^-27 kg.

Unpolarized light of intensity I₀ is incident on a polarizing filter. Light from this filter is incident on a second filter, which has its axis of polarization at 30˚ to that of the first filter.

The value of cos 30˚ is $\frac{\sqrt{3}}{2}$. What is the intensity of the light emerging through the second filter?

A. $\frac{\sqrt{3}}{2}$I₀

B. $\frac{3}{2}$I₀

C. $\frac{3}{4}$I₀

D. $\frac{3}{8}$I₀

A thin-walled cylinder of weight W, open at both ends, rests on a flat surface. The cylinder has a height L, an average radius R and a thickness x where R is much greater than x.

What is the pressure exerted by the cylinder walls on the flat surface?

A.  $\frac{W}{2\pi Rx}$

B.  $\frac{W}{\pi R^{2}x}$

C.  $\frac{W}{\pi R^2}$

D.  $\frac{W}{\pi R^{2}L}$

Two containers X and Y are maintained at the same temperature. X has volume $4 {\mathrm{m}}^3$ and Y has volume $6 {\mathrm{m}}^3$. They both hold an ideal gas. The pressure in X is $100 \mathrm{Pa}$ and the pressure in Y is $50 \mathrm{Pa}$. The containers are then joined by a tube of negligible volume. What is the final pressure in the containers?

A.  $70 \mathrm{Pa}$

B.  $75 \mathrm{Pa}$

C.  $80 \mathrm{Pa}$

D.  $150 \mathrm{Pa}$

The mass of a helium atom is 6.6 × 10^-27 kg. Estimate the average speed of the helium atoms in the container.

Calculate, in Pa, the new pressure of the gas.

Two identical containers X and Y each contain an ideal gas. X has N molecules of gas at an absolute temperature of T and Y has 3N molecules of gas at an absolute temperature of $\frac{T}{2}$ What is the ratio of the pressures $\frac{P_Y}{P_X}$?

A.   $\frac{1}{6}$

B.   $\frac{2}{3}$

C.   $\frac{3}{2}$

D.   $6$

A sealed cylinder of length l and cross-sectional area A contains N molecules of an ideal gas at kelvin temperature T.

What is the force acting on the area of the cylinder marked A due to the gas?

A.     $\frac{NRT}{l}$

B.     $\frac{NRT}{lA}$

C.     $\frac{N{k}_{B}T}{lA}$

D.     $\frac{N{k}_{B}T}{l}$

A container is filled with a mixture of helium and oxygen at the same temperature. The molar mass of helium is 4 g mol^–1 and that of oxygen is 32 g mol^–1.

What is the ratio $\frac{\text{average speed of helium molecules}}{\text{average speed of oxygen molecules}}$?

A.   $\frac{1}{8}$

B.   $\frac{1}{\sqrt{8}}$

C.   $\sqrt{8}$

D.   8

Calculate the volume of the oxygen produced in one second when it is allowed to expand to a pressure of 0.11 MPa and to reach a temperature of 260 K.

A substance in the gas state has a density about $1000$ times less than when it is in the liquid state. The diameter of a molecule is $d$. What is the best estimate of the average distance between molecules in the gas state?

A.  $d$

B.  $10d$

C.  $100d$

D.  $1000d$

A second container, of the same volume as the original container, contains twice as many helium atoms. The graph of the variation of P with T is determined for the gas in the second container.

Predict how the graph for the second container will differ from the graph for the first container.

0.46 mole of an ideal monatomic gas is trapped in a cylinder. The gas has a volume of 21 m³ and a pressure of 1.4 Pa.

(i) State how the internal energy of an ideal gas differs from that of a real gas.

(ii) Determine, in kelvin, the temperature of the gas in the cylinder.

(iii) The kinetic theory of ideal gases is one example of a scientific model. Identify two reasons why scientists find such models useful.

A fixed mass of an ideal gas in a closed container with a movable piston initially occupies a volume V. The position of the piston is changed, so that the mean kinetic energy of the particles in the gas is doubled and the pressure remains constant.

What is the new volume of the gas?

A.  $\frac{V}{4}$

B.  $\frac{V}{2}$

C.  2V

D.  4V

A sample of oxygen gas with a volume of $3.0 {\text{m}}^3$ is at $100 °\text{C}$. The gas is heated so that it expands at a constant pressure to a final volume of $6.0 {\text{m}}^3$. What is the final temperature of the gas?

A. $750 °\text{C}$

B. $470 °\text{C}$

C. $370 °\text{C}$

D. $200 °\text{C}$

Show that (p_o + p_m) × 0.190 = $\frac{nRT}{A}$  where

p_o = atmospheric pressure

p_m = pressure due to the mercury column

T = temperature of the trapped gas

n = number of moles of the trapped gas

A = cross-sectional area of the tube. 

Explain, in terms of molecular motion, this change in pressure.

Calculate, in J, the internal energy of the gas.

The cross-sectional area of the tube is 1.3 × 10^–3$$m² and the temperature of air is 300 K. Estimate the number of moles of air in the tube.

Rutherford and Royds expected 2.7 x 10¹⁵ alpha particles to be emitted during the experiment. The experiment was carried out at a temperature of 18 °C. The volume of cylinder B was 1.3 x 10^–5 m³ and the volume of cylinder A was negligible. Calculate the pressure of the helium gas that was collected in cylinder B.

The experiment was carried out at a temperature of 18 °C. The volume of cylinder B was 1.3 x 10^–5 m³ and the volume of cylinder A was negligible. Calculate the pressure of the helium gas that was collected in cylinder B over the 6 day period. Helium is a monatomic gas.

Determine, in kJ, the total kinetic energy of the particles of the gas.

Helium has a molar mass of 4.0 g. Calculate the mass of gas in the container.

Calculate the pressure of the gas.

A container is filled with 1 mole of helium (molar mass 4 g mol⁻¹) and 1 mole of neon (molar mass 20 g mol⁻¹). Compare the average kinetic energy of helium atoms to that of neon atoms.

Estimate the root mean square speed of nitrogen molecules in the Titan atmosphere. Assume an atmosphere temperature of 90 K.

Calculate the number of gas particles in the cylinder.