Entropy of a contained ideal gas mixture

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Heating an ideal gas mixture in a non-expanding container increases the entropy of the system. Although the gases cannot become more disordered in a confined space, the increase in temperature raises particle speeds, resulting in a greater number of possible microstates. This higher energy state contributes to the overall entropy increase. Therefore, even within a fixed volume, heating a gas mixture leads to increased entropy. Heating a system always results in an increase in entropy.
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If an ideal gas mixture is heated inside of a container which does not expand then does the entropy increase? Outside the container I know it would but inside the container the gases can't really become more disordered.
 
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But particle speeds are higher, so there are more possible speeds that any particular particle can assume. Heating thus provides more possible microstates.

Heating a system always increases its entropy.
 
thank you for the clarification!
 

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