Problem: Consider a system that consists of two standard playing dice, with the state of the system defined by the sum of the values shown on the top faces.The two arrangements of top faces shown here can be viewed as two possible microstates of the system. Which state or states have the highest entropy? Explain.

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We have to determine which of the two given microstates of the system has the higher entropy.


A specific way, in which the energy of a system can be arranged, is called a microstate. Each microstate has a different probability.


We have to first determine how many microstates of the given system are possible.

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Problem Details

Consider a system that consists of two standard playing dice, with the state of the system defined by the sum of the values shown on the top faces.
Two pairs of dice are shown.  The first pair shows a 1 and a 2, and the second pair shows a 4 and a 3.

The two arrangements of top faces shown here can be viewed as two possible microstates of the system. Which state or states have the highest entropy? Explain.

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Boltzmann Equation concept. If you need more Boltzmann Equation practice, you can also practice Boltzmann Equation practice problems.