## Internal Energy and Spontaneity

Volume: $\Delta S = nR\ln \frac{V_{2}}{V_{1}}$
Temperature: $\Delta S = nC\ln \frac{T_{2}}{T_{1}}$

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### Internal Energy and Spontaneity

When expanding the volume of a container full of gas in a vacuum, no work is done and so delta U is equal to zero. However, can someone explain why the gas expands spontaneously? Is it because of entropy, and why?

miznaakbar
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### Re: Internal Energy and Spontaneity

Spontaneously, a gas wants to occupy the greatest number of positions/states, meaning the entropy increases. Thus, the gas expands its volume to reach its maximum entropy without any change in heat, work, or internal energy.

Tia Tomescu 2D
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### Re: Internal Energy and Spontaneity

To add on to that, the system is at equilibrium when entropy is at a maximum.

Sirajbir Sodhi 2K
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### Re: Internal Energy and Spontaneity

The spontaneity of a reaction doesn't have a lot to do with internal energy, which is the thermodynamic potential. Only when S and V are constant will a spontaneous reaction reduce internal energy -- not at constant P or T. Rather, we need to look at Gibb's Free Energy which accounts for a non-constant enthalpy and entropy.

In this case, the gas expands as it wants to increase its entropy -- this cannot be predicted by internal energy, only Gibbs Free Energy.

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