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. 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. 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. 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. 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. 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?