Maximum value of the quantity of energy transfered in a linear process

In a linear process with an ideal gas, given by $p(V)=p_0-alpha V$ ($p$ – pressure, $V$ – volume) in the $pV$ coordinates, the quantity of energy ($Q=ΔU+W$) transfered between point $A$ (with the highest temperature) and an arbitrary point $B$, both on the $p(V)$ graph, reaches its maximum when $B$ is the point of tangency of the graph with an adiabat of the gas. Why is this true?