  We revisit the paradigm of an ideal gas under isothermal conditions. A moving
piston performs work on an ideal gas in a container that is strongly coupled to
a heat reservoir. The thermal coupling is modelled by stochastic scattering at
the boundaries. In contrast to recent studies of an adiabatic ideal gas with a
piston [R.C. Lua and A.Y. Grosberg, \textit{J. Phys. Chem. B} 109, 6805 (2005);
I. Bena et al., \textit{Europhys. Lett.} 71, 879 (2005)], container and piston
stay in contact with the heat bath during the work process. Under this
condition the heat reservoir as well as the system depend on the work parameter
$\lambda$ and microscopic reversibility is broken for a moving piston. Our
model is thus not included in the class of systems for which the
non-equilibrium work theorem has been derived rigorously either by Hamiltonian
[C. Jarzynski, \textit{J. Stat. Mech.} P09005 (2004)] or stochastic methods
[G.E. Crooks, \textit{J. Stat. Phys.} 90, 1481 (1998)]. Nevertheless the
validity of the non-equilibrium work theorem is confirmed both numerically for
a wide range of parameter values and analytically in the limit of a very fast
moving piston, i.e. in the far non-equilibrium regime.
