How much energy is needed to melt 0.225 kg of lead so that it can be used to make a lead sinker for fishing? The sample has an initial temperature of 27.3 degrees celsius and is poured in the mold immediately after it has melted.
Not sure if this is relevant to finding the answer but just incase:
Melting point of lead: 327.3 degrees celsius
Boiling point of lead: 1745 degrees celsius
Latent head of fusion for lead: 2.45 x 10^4 J/kg
Latent heat of vaporization for lead: 1.14 x 10^7 J/kg
I got something like 14,158 J.
You need to raise the temperature of the lead from 27.3 degrees C to 327.3 degrees C
heat required = mass * specific heat of lead * (327.3-27.3)
then melt the lead
heat to melt = mass * heat of fusion of lead
You know everything here but the specific heat of lead which you better look up.
To calculate the energy required to melt the lead, we need to consider the following steps:
1. Calculate the energy required to heat the lead from its initial temperature to its melting point.
2. Calculate the energy required to melt the lead at its melting point.
Step 1: Calculate the energy required to heat the lead
To do this, we use the specific heat capacity of lead, which is defined as the amount of energy required to raise the temperature of 1 kilogram of the substance by 1 degree Celsius.
The specific heat capacity of lead is not provided, but we can assume it to be approximately 130 J/kg·°C.
The temperature change required to heat the lead from its initial temperature of 27.3°C to its melting point of 327.3°C is:
ΔT = 327.3°C - 27.3°C = 300.0°C
The energy required to heat the lead is given by the equation:
Q = m * c * ΔT
where Q is the energy, m is the mass, c is the specific heat capacity, and ΔT is the temperature change.
Calculating the energy required to heat the lead:
Q1 = (0.225 kg) * (130 J/kg·°C) * (300.0°C)
Step 2: Calculate the energy required to melt the lead
The latent heat of fusion for lead is given as 2.45 x 10^4 J/kg. This represents the energy required to convert the lead from a solid state to a liquid state without any change in temperature.
The energy required to melt the lead is given by:
Q2 = m * L
where Q2 is the energy, m is the mass, and L is the latent heat of fusion.
Calculating the energy required to melt the lead:
Q2 = (0.225 kg) * (2.45 x 10^4 J/kg)
To find the total energy required to melt the lead, we add the energies calculated in steps 1 and 2:
Total energy = Q1 + Q2
Therefore, the total energy required to melt 0.225 kg of lead is equal to:
Total energy = Q1 + Q2
Note: Make sure to convert all the units to be consistent (e.g., mass in kilograms, temperature in Celsius, and latent heat of fusion in joules per kilogram).
Now, you can calculate the values and get the final answer.