Final answer:
A 0.5 kg sample of copper will demonstrate the greatest increase in temperature when 500 J of energy is added because the change in temperature is inversely proportional to the mass of the substance, given the specific heat capacity is constant.option (a).
Step-by-step explanation:
To determine which sample of copper would demonstrate the greatest increase in temperature when 500 J of energy is added, we can use the formula for heat transfer, which is Q = mcΔT, where Q is the heat added, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
Given that all samples are copper with a specific heat of 390 J/kg°C, adding the same amount of energy to samples of different masses will result in the smallest mass having the greatest increase in temperature, because Q and c are constant and ΔT is inversely proportional to m. Hence, a 0.5 kg sample of copper will have the greatest increase in temperature.