With respect to a gas, explain the meaning of the terms thermal energy and internal energy.

The graph shows how the pressure P of a sample of a fixed mass of an ideal gas varies with volume V. The gas is taken through a cycle ABCD.

V / 10^–6 m³

(i) Estimate the net work done during the cycle.

(ii) Explain whether the net work is done on the gas or by the gas.

(iii) Deduce, using the data from the graph, that the change C is isothermal.

(iv) Isothermal change A occurs at a temperature of 450 K. Calculate the temperature at which isothermal change C occurs.

(v) Describe the changes B and D.

(Q) energy transferred between two objects (at different temperatures);
(U) (total) potential energy and (random) kinetic energy of the molecules/particles (of the gas);

(i) use of area within cycle;
each large square has work value of 250 (J);
estimate (16 x 250= )4000 (J); (allow 3600 − 4100)
Award [3] for same outcome with small squares of area 10 (J).

(ii) (work is done by the gas because) area under expansion is greater than that under compression/pressure during expansion is greater than during compression;

(iii) clear attempt to compare two PV values;
evaluate two PV values correctly eg 75 x 80= 6000 and 200 x 30= 6000;  

(iv) use of PV =nRT or equivalent;
1350/1330 (K);

(v) both changes are isochoric/isovolumetric/constant volume changes;
B: temperature/internal energy increases, D: temperature/internal energy decreases;
B: thermal energy/heat input (to system), D: thermal energy/heat output (from system);
B: pressure increases, D: pressure decreases;

Few candidates were able to explain thermal energy was the energy transfer between two objects at different temperatures. Many knew the definition of internal energy but a high percentage omitted to mention the potential energy (probably assuming that the gas was ideal).

(i) Many candidates appeared to attempt to calculate area without actually saying what they were doing; although this was obvious when they referred to the area of a square, in many case it was not obvious and marks were lost when the candidates technique produced an answer out of tolerance. In examples like this there will be a reasonable tolerance for the area and it is not expected that candidates will waste considerable time in counting the small squares.

(ii) Although some candidates were aware that a clockwise cycle applies to net work done by the gas, this does not explain the choice. Simply saying that the area under the expansion was greater than the area under the compression was all that was needed.

(iii) This part was mostly well done by candidates. It is accepted, in line with SL A1, that showing constancy of two PV values does not prove that the change is isothermal; however in terms of deducing that the change is isothermal this technique is fine – that is, the candidates are told that it is isothermal and they are simply illustrating that this is the case. Often examiners will expect three values to be taken in questions such as this.

(iv) This part was well done by those many candidates who used any appropriate variant of the ideal gas equation to calculate the temperature.

(v) The large majority of candidates did well here although a minority were deducted marks when they used contradictory statements such as isochoric and compression or expansion.