Date | November 2018 | Marks available | 3 | Reference code | 18N.3.SL.TZ0.7 |
Level | Standard level | Paper | Paper 3 | Time zone | 0 - no time zone |
Command term | Show that | Question number | 7 | Adapted from | N/A |
Question
The pV diagram of a heat engine using an ideal gas consists of an isothermal expansion A → B, an isobaric compression B → C and an adiabatic compression C → A.
The following data are available:
Temperature at A = 385 K
Pressure at A = 2.80 × 106 Pa
Volume at A = 1.00 × 10–4 m3
Volume at B = 2.80 × 10–4 m3
Volume at C = 1.85 × 10–4 m3
Show that at C the pressure is 1.00 × 106 Pa.
Show that at C the temperature is 254 K.
Show that the thermal energy transferred from the gas during the change B → C is 238 J.
The work done by the gas from A → B is 288 J. Calculate the efficiency of the cycle.
State, without calculation, during which change (A → B, B → C or C → A) the entropy of the gas decreases.
Markscheme
ALTERNATIVE 1:
Pc=PB=PAVAVB ✔
= 2.8×106×1×10−42.8×10−4 «= 1.00 × 106 Pa» ✔
ALTERNATIVE 2:
2.8×106×1.0053=Pc×1.8553 ✔
Pc=2.8×106×1.00531.8553 «= 1.00 × 106 Pa» ✔
ALTERNATIVE 1:
Since TB = TA then Tc = VcTBVB ✔
= 1.85×3852.8 «= 254.4 K» ✔
ALTERNATIVE 2:
2.80×1.00385=1.00×1.85Tc «K»✔
Tc=385×1.00×1.852.80 «= 254.4 K» ✔
work done = «pΔV = 1.00 × 106 × (1.85 × 10−4 − 2.80 × 10−4 =» −95 «J» ✔
change in internal energy = «32pΔV = −32 × 95 =» −142.5 «J» ✔
Q = −95 − 142.5 ✔
«−238 J»
Allow positive values.
net work is 288 −238 = 50 «J» ✔
efficiency = «288−238288 =» 0.17 ✔
along B→C ✔