Question EXE.2.HL.TZ0.14
| Date | Example questions Example questions | Marks available | [Maximum mark: 7] | Reference code | EXE.2.HL.TZ0.14 |
| Level | HL | Paper | 2 | Time zone | TZ0 |
| Command term | Calculate, Determine, Estimate | Question number | 14 | Adapted from | N/A |
The table shows some of the macrostates and microstates for 10 identical coins tossed at random that can land either heads or tails upwards.
| Macrostate | Number of microstates | |
| heads | tails | |
| 10 | 0 | 1 |
| 9 | 1 | 10 |
| 8 | 2 | 45 |
| 7 | 3 | 120 |
| 6 | 4 | 210 |
| 5 | 5 | 252 |
There are a total of 1024 microstates for this system.
Determine the fractional number of throws for which the three most likely macrostates occur.
[3]
Recognises that 4 heads and 6 tails also required ✓
Total number of microstates = 672 ✓
Fractional number = 672/1024 = 0.66 ✓
Allow ecf for MP3
A throw is made once every minute. Estimate the average time required before a throw occurs where all coins are heads or all coins are tails.
[2]
Two chances in 1024 so once every 512 throws ✓
512 throws take 8.5 h so (a reasonable estimate is half way through) on average 4.3 h ✓
In one throw the coins all land heads upwards. The following throw results in 7 heads and 3 tails. Calculate, in terms of , the change in entropy between the two throws.
[2]
✓
✓