When two different gases are mixed under the same temperature and pressure, the entropy of the system increases.

Quick Scoop: What happens to entropy?

When two gases are kept separate, each set of molecules can only move and spread out in its own region. Once you remove the partition and let them mix, molecules of each gas can now explore the entire total volume, in many more possible arrangements.

In thermodynamic language, more possible microscopic arrangements means higher entropy (greater disorder or randomness). So, for mixing of ideal gases at constant temperature and pressure, the entropy change ΔSmix\Delta S_{\text{mix}}ΔSmix​ is positive: entropy goes up.

In multiple‑choice questions of the form
“When two gases are mixed the entropy: (A) remains constant (B) decreases (C) increases (D) becomes zero”
the correct answer is: increases.

Why does entropy increase when gases mix?

Think of each gas as a crowd in its own room. Open the door between the rooms and both crowds spread out everywhere. There are now vastly more ways to arrange the individuals, even though total energy and temperature can stay the same.

In statistical thermodynamics, this is captured by a standard “entropy of mixing” expression for ideal gases, which is always positive unless you are mixing identical gases (in which case there is effectively no real mixing and no entropy change).

Key points:

  • Mixing of different gases at fixed temperature and pressure is spontaneous because of the favorable increase in entropy.
  • The process is effectively irreversible in practice; the gases do not unmix on their own.
  • The more evenly the gases are present (similar amounts), the larger the entropy of mixing.

Mini FAQ style recap

  • Concept check: Entropy is a measure of randomness/disorder in a system.
  • State function: Entropy depends only on the initial and final states, not the path.
  • Phase order: S(solid)<S(liquid)<S(gas)S(\text{solid})<S(\text{liquid})<S(\text{gas})S(solid)<S(liquid)<S(gas), and mixing gases increases disorder further.

So, for the phrase “when two gases are mixed the entropy…”, the thermodynamically correct completion is:

“When two gases are mixed the entropy increases.”

TL;DR: When two different gases mix at the same temperature and pressure, the system’s entropy increases due to greater molecular randomness and more accessible volume for each gas.

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