A closed-form expression for the indicated work per cycle of a Schmidt gamma Stirling can be written in the following way:

where X and Y are the functions defined above in the set of Equations (10.1). Appendix C outlines the derivation of Equations (10.1) and (10.2). Note that the only factors having dimension in the expression for W are the combined or total swept volume of the piston and displacer, V _T = V ₁ + V ₂ = ( ? + 1) V ₁, and , the root mean of the maximum and minimum cycle pressures, which also equals the integral average pressure. For simplicity in this treatment, all the dead space is treated as being at the arithmetic average of the extreme cycle temperatures; this is reflected in the last term of the parameter Y which involves the dead space ratio ?.