Question #2978

What is the equation for work done in a reversible isothermal process (processes 1 to 3 in this case)? My course tutor wrote down (P3V3)ln(V1/V3), what is this?

Expert's answer

The expression of work for that process

**A=-nRT*ln(V**_{3}/V_{1})

where V_{1}-the initial volume, V_{3} -the final volume.

From the equation of state, if our substance is a gas we can get an approximate value of the expansion work using the ideal gas equation of state

**pV=nRT**

Since T=const, we can say that**nRT=p**_{3}V_{3}

also from the properties of ln-function

**ln(V**_{3}/V_{1})=-ln(V_{1}/V_{3})

So we have

**A=p**_{3}V_{3}*ln(V_{1}/V_{3}) that's exactly what ur teacher wrote.

where V

From the equation of state, if our substance is a gas we can get an approximate value of the expansion work using the ideal gas equation of state

Since T=const, we can say that

also from the properties of ln-function

So we have

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