Question

Show that w and q for an arbitrary mechanically reversible non flow process are given by

Answer 1

is really a mathematical exercise on integration by parts.

W=−∫PdV=−(ΔPV−∫VdP)=∫VdP−ΔPVW=−∫PdV=−(ΔPV−∫VdP)=∫VdP−ΔPV

Q=U−W=ΔU−(∫VdP−ΔPV)=ΔU+ΔPV−∫VdP=ΔH−∫VdPQ=U−W=ΔU−(∫VdP−ΔPV)=ΔU+ΔPV−∫VdP=ΔH−∫VdP

hope helps ☺️

Answer 2

This is really a mathematical exercise on integration by parts.

W=−∫PdV=−(ΔPV−∫VdP)=∫VdP−ΔPVW=−∫PdV=−(ΔPV−∫VdP)=∫VdP−ΔPV

Q=U−W=ΔU−(∫VdP−ΔPV)=ΔU+ΔPV−∫VdP=ΔH−∫VdPQ=U−W=ΔU−(∫VdP−ΔPV)=ΔU+ΔPV−∫VdP=ΔH−∫VdP