We investigate the work dissipated during the irreversible unfolding of single molecules by mechanical force, using the simplest model necessary to represent experimental data. The model consists of two levels (folded and unfolded states) separated by an intermediate barrier. We compute the probability distribution for the dissipated work and give analytical expressions for the average and variance of the distribution. To first order, the amount of dissipated work is directly proportional to the rate of application of force (the loading rate) and to the relaxation time of the molecule. The model yields estimates for parameters that characterize the unfolding kinetics under force in agreement with those obtained in recent experimental results. We obtain a general equation for the minimum number of repeated experiments needed to obtain an equilibrium free energy, to within kBT, from nonequilibrium experiments by using the Jarzynski formula. The number of irreversible experiments grows exponentially with the ratio of the average dissipated work, Wdis to kBT.