| Date | May 2012 | Marks available | 3 | Reference code | 12M.2.HL.TZ2.8 |
| Level | Higher level | Paper | Paper 2 | Time zone | Time zone 2 |
| Command term | Estimate | Question number | 8 | Adapted from | N/A |
Question
Part 2 Thermodynamic cycles
A gas undergoes a thermodynamic cycle. The P–V diagram for the cycle is shown below.
In the changes of state B to C and D to A, the gas behaves as an ideal gas and the changes in state are adiabatic.
(i) State the circumstances in which the behaviour of a gas approximates to ideal gas behaviour.
(ii) State what is meant by an adiabatic change of state.
With reference to the first law of thermodynamics, explain for the change of state A to B, why energy is transferred from the surroundings to the gas.
Estimate the total work done in the cycle.
Markscheme
(i) low pressure;
high temperature;
(ii) no thermal/heat energy is transferred (in change of state);
Allow “heat energy” but not “heat”.
work is done (by the gas) because there is an increase in volume/gas expands;
so W is positive;
ΔU is greater than zero (because P is constant and V increases);
from first law Q=ΔU+W means that Q is positive which means energy transferred into gas;
total work done = enclosed area / number of large squares ∼40(±5);
1 square=5 J;
work done=200J (±25) J;
Examiners report
(i) Some candidates simply repeated the information they had already supplied in A4(a) without thinking the problem through afresh. The correct ideas of low pressure and high temperature were commonly seen in scripts.
(ii) Many recognized that adiabatic changes involve no energy interchange. Those who talked about no exchange of heat were penalized. The bald term “heat” is not awarded credit in this examination.
This was often well done with perhaps a third of the candidates gaining full or near-full marks for recognition of the work done and a deduction from this of the sign of ΔU and W.
Although about half were able to arrive at a close estimate of the work done in the cycle, sometimes explanations were brief and obscure. A string of numbers without explanation does not endear itself to the examiners who can only rarely give credit to partial solutions if it is not clear what ideas are in use or where the data is coming from.
