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Usually the problem will tell you. If not, in reversible expansion, the pressure of the system equals the external pressure (which decreases during the expansion). In irreversible expansion, the external pressure is constant.
In irreversible expansion, there is a sudden significant change in external pressure that allows the contents of the system to expand. In a reversible expansion, external pressure is reduced gradually and in small increments so that Pexternal = Psystem. Usually in problems it will state whether it is a reversible or irreversible reaction.
Nick Lewis 4F wrote:How can you differentiate when to use -nRlnV2/V1 versus using -PV? I feel like I always get mixed up when I should use which equation. Any tips for knowing which one to use when?
this is the link to a chart that a TA made that really helped me distinguish which equation to use when
Generally the problem should specify which one it is. If not, for a reversible expansion, Psystem = external pressure, which will decrease as the expansion takes place. For an irreversible expansion, the external pressure will be constant.
In an irreversible expansion, the external pressure on something has changed a huge (relative) amount in a short span of time. For an irreversible expansion, the external pressure is constant. For a reversible expansion, the internal and external pressure change in small, infinitesimal increments so that when the internal pressure changes, the external pressure reacts to that change in a similar way (and vice versa). This means that the internal pressure (pressure of the system) equals the external pressure the whole way through (Psystem = Pexternal). When given a problem about gaseous expansion, the problem will tell you whether it is an irreversible or a reversible expansion.
In addition to what has already been said, for a reversible expansion, there is heat transfer to maintain the temperature. However, for an irreversible expansion, there is no heat transfer because the change occurs too quickly.
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