Final answer:
To determine the minimum work required of a refrigerator, we can use the coefficient of performance formula. By substituting the given values into the formula, we can calculate the work required.
Step-by-step explanation:
To determine the minimum work required of a refrigerator, we can use the formula for the coefficient of performance (COP) which relates the amount of heat extracted from the inside of the freezer to the work done by the refrigerator. The formula is: COP = Q_h / W, where Q_h is the heat extracted from the hot reservoir and W is the work done by the refrigerator.
In this case, Q_h = 50 J and the temperatures are given as -10 °C and 25 °C. Using the formula COP = Q_h / W and the known temperatures, we can calculate the work required.
By substituting the values into the formula, we get: COP = 50 J / W = T_c / (T_h - T_c). Rearranging the formula to solve for W, we have: W = Q_h / COP = Q_h * (T_h - T_c) / T_c.