| Date | November 2017 | Marks available | 2 | Reference code | 17N.3.SL.TZ0.8 |
| Level | Standard level | Paper | Paper 3 | Time zone | Time zone 0 |
| Command term | Show that | Question number | 8 | Adapted from | N/A |
Question
A monatomic ideal gas is confined to a cylinder with volume 2.0 x 10–3 m3. The initial pressure of the gas is 100 kPa. The gas undergoes a three-step cycle. First, the gas pressure increases by a factor of five under constant volume. Then, the gas expands adiabatically to its initial pressure. Finally it is compressed at constant pressure to its initial volume.
Show that the volume of the gas at the end of the adiabatic expansion is approximately 5.3 x 10–3 m3.
Using the axes, sketch the three-step cycle.
The initial temperature of the gas is 290 K. Calculate the temperature of the gas at the start of the adiabatic expansion.
Using your sketched graph in (b), identify the feature that shows that net work is done by the gas in this three-step cycle.
Markscheme
\(500\,000 \times {\left( {2 \times {{10}^{ - 3}}} \right)^{\frac{5}{3}}} = 100\,000 \times {V^{\frac{5}{3}}}\)
V = 5.3 x 10–3 «m3»
Look carefully for correct use of pVγ = constant
correct vertical and horizontal lines
curve between B and C
Allow tolerance ±1 square for A, B and C
Allow ECF for MP2
Points do not need to be labelled for marking points to be awarded
use of PV = nRT OR use of \(\frac{P}{T}\) = constant
T = «5 x 290 =» 1450 «K»
area enclosed
work is done by the gas during expansion
OR
work is done on the gas during compression
the area under the expansion is greater than the area under the compression
