Two physics students decide to play a game of statistics in order to simulate what…
MATHEMATICS · Multi-part · ISC · Mathematics · Probability · Statistics and Probability
Problem
Two physics students decide to play a game of statistics in order to simulate what happens when a hot body is put into thermal contact with a cold body. Amaya models a hot body by having 60 counters, whilst Andrew models a cold body by having six counters. Each counter represents a small amount of energy. When the two bodies are brought into contact, the two students throw a six-sided spinner for each counter they have. If the spinner shows a six, the counter is passed to the other student.
(a) After one ‘turn’ of the game,
- i how many counters might statistically be expected to be given to Andrew?
- ii how many counters might statistically be expected to be given to Amaya?
- iii how many counters will Amaya and Andrew now have?
- iv what has happened to the ‘temperature’ of Amaya and of Andrew’s bodies?
(b) After another ‘turn’,
- i how many counters might statistically be expected to be given to Andrew?
- ii how many counters might statistically be expected to be given to Amaya?
- iii how many counters will Amaya and Andrew now have?
- iv what has happened to the ‘temperature’ of Amaya and of Andrew’s bodies?
(c) After a large number of turns,
- i what would you statistically expect to have happened to Amaya’s and Andrew’s counters?
- ii what would you say has happened to their temperatures?
(d) If Amaya and Andrew continued to play the game,
- i would they still exchange counters on each turn?
- ii how would Amaya and Andrew explain that their two bodies are in thermal equilibrium?
(e) After playing the game, Amaya and Andrew are happy that the game does simulate what happens in real life when a hot body is brought into contact with a cold body.
- i How do the two students explain why the hotter body cools and the colder body warms?
- ii How would the two students explain why the hotter body doesn’t become even hotter and the colder body become even colder? That is why isn’t there a net transfer of energy from the colder body to the hotter body?