You have a 4.5 kg lead block at room temperature. Find the energy required to raise the lead's temperature to its melting point. Find the energy required to melt the lead once it's reached the melting point.
To find the energy required to raise the lead's temperature to its melting point, we need to use the specific heat capacity of lead.
The specific heat capacity of lead, denoted as C, is approximately 0.13 J/g°C or 130 J/kg°C.
Step 1: Convert the mass of the lead block to grams:
4.5 kg = 4,500 grams
Step 2: Determine the temperature difference between the current temperature and the melting point of lead. Let's assume the current temperature is 25°C and the melting point of lead is 327°C.
Temperature difference = (327°C - 25°C) = 302°C
Step 3: Calculate the energy required to raise the lead's temperature to its melting point:
Energy = Mass x Specific Heat Capacity x Temperature Difference
Energy = 4,500 g x (130 J/kg°C) x 302°C
Calculating this gives us:
Energy = 1,137,900 J or approximately 1.14 x 10^6 J
Therefore, the energy required to raise the lead's temperature to its melting point is approximately 1.14 x 10^6 Joules.
Now, let's find the energy required to melt the lead once it has reached its melting point.
The heat energy required to melt a substance can be calculated using the latent heat of fusion (Lf), which is the amount of energy required to change a substance from a solid to a liquid at constant temperature and pressure. For lead, its latent heat of fusion is approximately 24,000 J/kg.
Step 4: Calculate the energy required to melt the lead once it has reached the melting point:
Energy = Mass x Latent Heat of Fusion
Energy = 4,500 g x (24,000 J/kg)
Calculating this gives us:
Energy = 108,000,000 J or approximately 1.08 x 10^8 J
Therefore, the energy required to melt the lead once it has reached its melting point is approximately 1.08 x 10^8 Joules.
To find the energy required to raise the lead's temperature to its melting point, you can use the specific heat capacity formula:
Q = mcΔT
Where:
Q is the energy required (in Joules),
m is the mass of the lead block (in kilograms),
c is the specific heat capacity of lead (in Joules per kilogram per degree Celsius), and
ΔT is the change in temperature (in degrees Celsius).
Since the lead block is initially at room temperature and we want to raise its temperature to its melting point, ΔT will be the difference between the melting point of lead and the initial temperature.
The specific heat capacity of lead is approximately 130 J/(kg·°C), and the melting point of lead is 327.5 °C.
Therefore, the energy required to raise the lead's temperature to its melting point can be calculated as follows:
Q = (4.5 kg) * (130 J/(kg·°C)) * (327.5 °C - initial temperature)
To find the energy required to melt the lead once it reaches the melting point, you can use the formula:
Q = mL
Where:
Q is the energy required (in Joules),
m is the mass of the lead block (in kilograms), and
L is the latent heat of fusion for lead (in Joules per kilogram).
The latent heat of fusion for lead is approximately 24,500 J/kg.
Therefore, the energy required to melt the lead once it reaches the melting point can be calculated as follows:
Q = (4.5 kg) * (24,500 J/kg)
By substituting the appropriate values, you can calculate both the energy required to raise the lead's temperature to its melting point and the energy required to melt the lead.