PX154 - E1 - work done along different paths in the pV diagram

PX154 - C2 - pV diagrams
any point on the $p V$ diagram has a specific values of $p$ and $V$
these then specify the temperature, and hence, the internal energy at that point
take either path 1 ( $i s o b a r \to i s o c h o r e$ ), or path 2 $(i s o c h o r e \to i s o b a r$ ) from $A \to B$ :
- $Δ U$ is the same for both the paths
- for $A \to X \to B : W = p_{1} (V_{2} - V_{1}) + 0$
- for $A \to Y \to B : W = 0 + p_{2} (V_{2} - V_{1})$
- but $p_{2} < p_{1} : W_{A Y B} < W_{A X B}$ , and $Q_{A Y B} < Q_{A X B}$
  $∴ Δ U$ is the same, but $Q$ and $W$ are different