To determine the heat capacity of the iron sample, we can use the formula:q = mcTwhere q is the heat energy in joules , m is the mass of the sample in grams , c is the specific heat capacity in J/gC , and T is the change in temperature in C .We are given the mass m = 50 g , the initial temperature 25C , the final temperature 100C , and the heat energy q = 500 J . We need to find the specific heat capacity c of the iron sample.First, let's calculate the change in temperature T :T = T_final - T_initialT = 100C - 25CT = 75CNow, we can rearrange the formula to solve for the specific heat capacity c :c = q / mT Plugging in the given values:c = 500 J / 50 g 75C c = 500 J / 3750 gCc = 0.133 J/gCThe heat capacity of the 50-g sample of iron is 0.133 J/gC.