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The distribution functions of the work performed on a two-dimensional Ising model under the influence of an external magnetic field which is switched on and off are studied. These distributions are calculated by means of Monte Carlo simulations for temperatures below and above, as well as close to the critical temperature, T_c, and for different rates of the switching processes. For this system the Jarzynski and the Crooks fluctuation theorems are verified. It is found that Crooks fluctuation theorem provides a faster method for evaluating free energy differences in this system with respect to the Jarzynski equality. As expected, for temperatures far from T_c the convergence of the results is faster than for T similar or equal to T_c, where a slower switching rate is needed. Results obtained from the theorems of Crooks and Jarzynski are compared with thermodynamic integration calculations and it is found that they agree very well within error bars.