how much energy would it take to melt 250kg of lead assuming it starts at 30 degrees centigrade.

To calculate the energy required to melt 250 kg of lead, we need to consider two steps: raising the temperature from 30 degrees Celsius to the melting point of lead, and then providing the heat of fusion to melt the lead at its melting point.

Let's break it down step by step:

Step 1: Calculate the energy required to raise the temperature from 30 degrees Celsius to the melting point of lead.

The specific heat capacity of lead is approximately 128 Joules per kilogram-kelvin (J/kg-K), meaning it takes 128 J of energy to raise the temperature of 1 kg of lead by 1 degree Celsius.

The melting point of lead is 327.5 degrees Celsius. So, we need to calculate the energy required to raise the temperature of 250 kg of lead by (327.5 - 30) degrees Celsius:

Energy = mass * specific heat capacity * change in temperature
= 250 kg * 128 J/kg-K * (327.5 - 30) K

Step 2: Calculate the energy required to melt the lead at its melting point.

The heat of fusion (also known as latent heat) of lead is approximately 24,000 Joules per kilogram (J/kg). This represents the energy required to change the state of 1 kg of lead from solid to liquid at its melting point.

So, we need to calculate the energy required to melt 250 kg of lead, converted into joules:

Energy = mass * heat of fusion
= 250 kg * 24,000 J/kg

Finally, we can calculate the total energy required:

Total energy = Energy to raise the temperature + Energy to melt the lead

Once calculated, you can add the two energy values together to find out how much energy is needed to melt 250 kg of lead starting at 30 degrees Celsius.