Ideal gases and the gas laws

State why thermal energy passes into the tank.

Explain, in terms of particle energies, why the temperature of the oxygen remains constant despite the transfer of thermal energy into the tank.

Show that in one hour the volume of liquid oxygen that evaporates is about 0.02 m³. (c)

After one hour the number of moles of gas above the remaining liquid oxygen is 710.

Calculate the pressure of the gas.

Plot the missing data point on the graph above and draw a line of best fit.

Describe the relationship suggested by the graph and suggest an explanation.

An experiment is carried out to estimate the value of absolute zero using the variation of gas pressure with temperature. The apparatus is shown below.

Which variable must be controlled during the experiment?

A Pressure of the gas

B Temperature of the gas

C Volume of the gas

D None of the above

Your answer

A sealed container contains n moles of an ideal gas. The gas has pressure p, absolute temperature T and occupies volume V.

The mass of one mole of the gas is M.

Use an ideal gas equation to show that the density of the gas is given by the expression

An airship has a cabin suspended underneath a gasbag inflated with helium.

The airship is floating above the ground and is stationary.

The volume of the gasbag is 12 000 m³. The temperature of the helium and the surrounding air is 20 °C. Atmospheric pressure is 1.0 × 10⁵ Pa. The molar mass of air is 0.029 kg mol^–1. The volume of the cabin is negligible compared to the volume of the gasbag.

Show that the density of air under the conditions described is about 1.2 kg m^–3. (i)

Calculate the weight of air displaced by the airship.

weight of air........ N

Explain why the weight of air displaced by the airship has the same magnitude as the weight of the airship and its contents.

The pressure of the helium in the gasbag is maintained at a value only slightly greater than atmospheric pressure. Suggest why a larger pressure is not used.

The airship engine drives a fan which moves 7.8 kg of air per second at a relative speed of 45 m s^–1, so the airship starts to move.

All other conditions given in (b) remain the same.

Calculate the thrust that the engine produces.

The airship has a higher maximum speed at high altitudes, but also produces less thrust from the engine.

Explain these observations.

A kiln used to harden ceramics is shown below.

The internal chamber is a cube. Each side of this cube has length 0.46 m. The chamber is sealed and full of argon. Argon behaves as an ideal gas.

The kiln is initially at 20 C. The argon in the kiln has an initial pressure of 100 kPa.

Calculate the amount of argon n in the chamber in moles.

The temperature of the kiln is increased from 20 C to 1300 C.

Calculate the pressure in kPa at 1300 C.

The temperature of the kiln is 1300 C. A single atom of argon is travelling horizontally towards the vertical side X of the chamber. The initial speed of this atom is 990 m s^–1. After collision, it rebounds at the same speed.

Calculate the change in momentum p of this atom.

• mass of argon atom = 6.6 × 10^–26 kg

=........ kg m s^–1 p

Assume that this atom does not collide with any other argon atoms inside the chamber. Instead, it travels horizontally, making repeated collisions with the opposite vertical walls of the chamber.

1 Show that the atom makes about 1000 collisions with side X in a time interval of 1.0 s.

2 Calculate the average force F on side X made by the atom.

Without calculation, explain how your answer to (ii)2 could be used to estimate the total pressure exerted by the atoms of the argon gas in the kiln.

Use the kinetic theory of matter to describe the solid phase (section AB) and the liquid phase (section CD) in terms of the motion and arrangement of the molecules of the substance.

Use Fig. 21 to explain how the specific heat capacity of the liquid compares with the specific heat capacity of the solid.

State what is meant by the internal energy of the substance.

Beyond the point E in Fig. 21, the substance behaves as an ideal gas.

The mass of a gas molecule is 4.8 × 10^–26 kg. (i) Calculate the root mean square speed of the gas molecules at a temperature of 250 °C.

root mean square speed =........ m s^–1

Calculate the internal energy of 1.3 moles of the gas at 250 °C.

A toy rocket is made from a 1.5 litre plastic bottle with fins attached for stability.

The bottle initially contains 0.30 litres of water, leaving 1.2 litres of trapped air at a temperature of 17 °C. A pump is used to increase the pressure of the air within the plastic bottle to 2.4 × 10⁵ Pa at the start of lift-off.

Fig. 1.1 shows the rocket at the start of lift-off.

1 litre = 10^–3 m³

Calculate, in moles, the amount of trapped air in the bottle at the start of lift-off.

The trapped air pushes the water downwards out of the hole, causing the rocket to rise. The temperature of this air remains constant.

Calculate the final pressure of the trapped air just before all the water has been released.

Use the data above to show that the upwards force on the rocket at the start of lift-off is about 15 N.

Hence calculate the initial vertical acceleration of the rocket.

initial acceleration =........ m s^–2

Discuss whether adding more water initially would enable the rocket to reach a greater height.

A group of students are conducting an experiment in the laboratory to determine the value of absolute zero by heating a fixed mass of gas. The volume of the gas is kept constant. Fig. 17.1 shows the arrangement used by the students.

The gas is heated using a water bath. The temperature of the water is increased from 5 °C to 70 °C. The temperature of the water bath is assumed to be the same as the temperature of the gas. The pressure p of the gas is measured using a pressure gauge.

The results from the students are shown in a table.

/ °C	p / kPa
5 ± 1	224 ± 3
13 ± 1	231 ± 3
22 ± 1	238 ± 3
35 ± 1	248 ± 3
44 ± 1
53 ± 1	262 ± 3
62 ± 1	269 ± 3
70 ± 1	276 ± 3

Describe and explain how the students may have made accurate measurements of the temperature .

Fig. 17.2 shows the pressure gauge. Measurements of p can be made using the kPa scale or the psi (pounds per square inch) scale. The students used the psi scale to measure pressure and then converted the reading to pressure in kPa.

Suggest why it was sensible to use the psi scale to measure p.

Plot the missing data point and the error bars on Fig. 17.3.

* Explain what is meant by absolute zero. Describe how Fig. 17.3 can be used to determine the value of absolute zero. Determine the value of absolute zero. You may assume that the gas behaves as an ideal gas.

Describe, without doing any calculations, how you could use Fig. 17.3 to determine the actual uncertainty in the value of absolute zero in (c)(ii).

The experiment is repeated as the water bath quickly cools from 70 °C to 5 °C. Absolute zero was found to be −390 °C.

Compare this value with your value from (c)(ii) and explain why the values may differ. Describe an experimental approach that could be taken to avoid systematic error in the determination of absolute zero.