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
To find the energy needed to melt the lead, you need to calculate the energy required for two steps: raising the temperature from 27.3 degrees celsius to the melting point of 327.3 degrees celsius, and then the energy needed to undergo fusion (melting).
Step 1: Calculating the energy required to raise the temperature.
The specific heat capacity (c) of lead is required to determine the energy required to raise the temperature. Given that the initial temperature (T_initial) is 27.3 degrees celsius and the final temperature (T_melting) is 327.3 degrees celsius, you can subtract the initial temperature from the melting temperature to find the change in temperature (ΔT = T_melting - T_initial).
Next, you can use the formula:
Q = m * c * ΔT,
where:
Q is the energy required,
m is the mass of the lead (0.225 kg),
c is the specific heat capacity of lead (which you need to find), and
ΔT is the change in temperature.
Once you have calculated the value of c, you can substitute the values into the formula and find the energy required to raise the temperature.
Step 2: Calculating the energy required for fusion.
Given that the latent heat of fusion for lead (Lf) is 2.45 x 10^4 J/kg, you can use the formula:
Q = m * Lf,
where:
Q is the energy required, and
m is the mass of the lead (0.225 kg).
By substituting the values, you can find the energy required for fusion.
Finally, to get the total energy required to melt the lead for the fishing sinker, you need to add the values obtained from step 1 and step 2.
Remember to convert all temperatures to Kelvin before performing calculations, as the specific heat capacity is usually given in units of J/(kg·K).