The time constant of the RC circuit will decide how long the capacitor can supply the current to the load. As you are saying a 2.5W load with 24V operation, the resistive load for this would be (24^2)/ 2.5 = 230.4 ohm. Now with the capacitor of 470uF and 230.4 ohm load, one time constant will be RC = 108 msec. The capacitor will get fully discharged in 5 time constants = 541 msec.
As the capacitor discharges providing the load current, the voltage across the capacitor also drops exponentially. The instantaneous voltage can be calculated by the formula: Vb X exp(- t/RC). Where Vb will be 24V initial voltage, t is time instance, R is load resistance and C is capacitance.
For example the instantaneous voltages at 10msec, 15 msec, 100 mesc and 150 msec will be 21.9V, 15.1V, 9.53 and 6V.