To solve this problem, we can use the efficiency formula for a heat engine:
Efficiency = Work output / Heat input
Given that the efficiency is 25% (0.25) and the work output is 625 J, we can rearrange the formula to find the heat input:
Heat input = Work output / Efficiency
Heat input = 625 J / 0.25
Heat input = 2500 J
Now, we can determine the heat given off to the cold reservoir by using the first law of thermodynamics:
Heat input = Heat output + Work output
Since the heat input is 2500 J and the work output is 625 J, we can rearrange the formula to find the heat output:
Heat output = Heat input - Work output
Heat output = 2500 J - 625 J
Heat output = 1875 J
Therefore, the heat absorbed from the hot reservoir is 2500 J, and the heat given off to the cold reservoir is 1875 J.