Final answer:
To raise the temperature and melt 0.500 kg of lead, we need a total heat transfer of 1677 J.
Step-by-step explanation:
To calculate the amount of heat transfer needed to raise the temperature and melt 0.500 kg of lead, we can use the specific heat capacity and heat of fusion of lead. The specific heat capacity of lead is 0.130 J/g°C, and the heat of fusion is 24.5 J/g.
First, we need to calculate the heat required to raise the temperature of the lead from 25.0°C to its melting point, which is 327.5°C.
This can be calculated using the formula Q = m * c * ΔT, where Q is the heat transfer, m is the mass, c is the specific heat capacity, and ΔT is the temperature change. Plugging in the values, we get Q1 = (0.500 kg) * (0.130 J/g°C) * (327.5°C - 25.0°C).
The heat transfer required to raise the temperature is 1664.75 J.
Next, we need to calculate the heat required to melt the lead. This can be calculated using the formula Q = m * Hf, where Q is the heat transfer, m is the mass, and Hf is the heat of fusion.
Plugging in the values, we get Q2 = (0.500 kg) * (24.5 J/g). The heat transfer required to melt the lead is 12.25 J.
Adding the heat transfers together, the total heat transfer required to raise the temperature and melt 0.500 kg of lead is Q1 + Q2 = 1664.75 J + 12.25 J = 1677 J. So the correct answer is (a) 15,000 J.