| Date | May 2012 | Marks available | 3 | Reference code | 12M.2.SL.TZ2.4 |
| Level | Standard level | Paper | Paper 2 | Time zone | Time zone 2 |
| Command term | State | Question number | 4 | Adapted from | N/A |
Question
This question is in two parts. Part 1 is about ideal gases and specific heat capacity. Part 2 is about simple harmonic motion and waves.
Part 1 Ideal gases and specific heat capacity
State two assumptions of the kinetic model of an ideal gas.
Argon behaves as an ideal gas for a large range of temperatures and pressures. One mole of argon is confined in a cylinder by a freely moving piston.
(i) Define what is meant by the term one mole of argon.
(ii) The temperature of the argon is 300 K. The piston is fixed and the argon is heated at constant volume such that its internal energy increases by 620 J. The temperature of the argon is now 350 K.
Determine the specific heat capacity of argon in J kg–1 K–1 under the condition of constant volume. (The molecular weight of argon is 40)
At the temperature of 350 K, the piston in (b) is now freed and the argon expands until its temperature reaches 300 K.
Explain, in terms of the molecular model of an ideal gas, why the temperature of argon decreases on expansion.
Markscheme
point molecules / negligible volume;
no forces between molecules except during contact;
motion/distribution is random;
elastic collisions / no energy lost;
obey Newton’s laws of motion;
collision in zero time;
gravity is ignored;
(i) the molecular weight of argon in grams / 6.02×1023 argon
atoms / same number of particles as in 12 g of C-12;
(allow atoms or molecules for particles)
(ii) mass of gas = 0.040kg ;
specific heat = \(\frac{Q}{{m\Delta T}}\) or 620 = 0.04×c×50;
(i.e. correctly aligns substitution with equation)
\( = \left( {\frac{{620}}{{0.040 \times 50}} = } \right)310{\rm{Jk}}{{\rm{g}}^{{\rm{ - 1}}}}{{\rm{K}}^{{\rm{ - 1}}}}\);
temperature is a measure of the average kinetic energy of the molecules;
(must see “average kinetic” for the mark)
energy/momentum to move piston is provided by energy/momentum of molecules that collide with it;
the (average) kinetic energy of the gas therefore decreases;
Do not allow arguments in terms of loss of speed as a result of collision with a moving piston.
Examiners report
Many could only give one sensible assumption of the ideal gas kinetic model. It was very common to see the bald statement that there are no interatomic forces between the molecules. Candidates failed to give the proviso that this is not true during the collisions between molecules and with the walls of the container. Some candidates tried unsuccessfully to convince examiners that the empirical gas laws are in themselves assumptions.
(i) Many could either define the mole of argon in terms of 12 g of carbon-12 or in terms of a correctly stated Avogadro number. Either was acceptable if clear.
(ii) Although almost all were able to identify the starting point for the calculation of the specific heat capacity of argon, a very common error was to forget that the molar mass is quoted in grams not kilograms. It was therefore common to see answers that were 1000 times too small.
Explanations for the decrease in temperature of the gas on expansion were weak. The key to the explanation is that, at the molecular level, temperature is a measure of the average kinetic energy of the particles. This was often missing from the answers..
