Capillary bridging can generate substantial forces between solid surfaces. Impacted technologies and sciences include micro- and nanomachining, disk drive interfaces, scanning probe microscopy, biology, and granular mechanics. Existing calculations of the rupture work of capillary bridges do not consider the thermodynamics relating to the evaporation that can occur in the case of volatile liquids. Here, we show that the occurrence of evaporation decreases the rupture work by a factor of about 2. The decrease arises from heat taken from the surroundings that is converted into work. The treatment is based on a thermodynamic control-volume analysis of the pendular bridge geometry. We extend the mathematical formulation of Orr et al., solving the meniscus problem exactly for non-wetting surfaces. The extension provides analytical results for conditions at the rupture point and at a possible inflection point and for the rupture work. A simple equation (eq 32) is shown to fit the rupture work for the two cases over a meniscus curvature range of 3 orders of magnitude. Coefficients for the equation are given in tabular form for different contact angle pairs.