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CAF123

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## Homework Statement

An ideal gas undergoes the following reversible cycle: (a) an isobaric expansion from (P1, V1) to (P1, V2), (b) an isochoric reduction from (P1, V2) to (P2, V2) (c) an isobaric reduction from (P2, V2) tp (P2, V1) (d) an isochoric expansion from (P2,V1) to (P1, V1). What work is done in this cycle? How much work is done by the gas in traversing the cycle 100 times?

## Homework Equations

Work done by gas/surroundings: $$W = - \int_{V_1}^{V_2} P\,dV$$

## The Attempt at a Solution

No work done in cases (b), (d). In case (a), assuming the gas is expanding against the surroundings, W = -P1(V2-V1) (My book uses convention that negative work for system doing work on surroundings)

In case (c), surroundings do work on gas, acting to compress, so W = -P2(V1-V2).

Work done in cycle presumably refers to net work in cycle? In which case net work, ##W_N = -P_1(V_2 - V_1) - P_2(V_1 - V_2).## Is this correct? My book has the work done by gas = (P1 - P2)(V2 - V1). How can this be correct? The only work done by the gas is in step (a) of the cycle?

Many thanks