Answer: The specific heat of the metal can be calculated using the formula Q = mcΔT, where Q is the heat absorbed by the metal, m is the mass of the metal, c is the specific heat of the metal, and ΔT is the change in temperature. Since we know the heat absorbed by the metal (10,000 joules) and the mass of the metal (200 grams), we can solve for the specific heat by rearranging the equation to solve for c:
Q = mcΔT
c = Q / mΔT
c = (10,000 joules) / (200 grams * 80 degrees Celsius)
c = 0.625 joules/gram-degree Celsius
Therefore, the specific heat of the metal is 0.625 joules/gram-degree Celsius, which corresponds to answer choice (c).