lead has specific heat of .028kcal/kgC, melting point of 328 degrees C and a heat fusion of 5.5 kcal/kg. how much heat must be provided to melt a 250kg sample of lead with a temperature of 20 degrees Celsius?

Q = M*[C*(delta T) + H]

detlta T = 308 C
H = 5.5 kcal/kg
C = 0.028 kcal.kg*C
M = 250 kg

Do the calculation for the heat (Q) in kcal

to get the heat released or absorbed,

Q = mc(T2-T1)
where
m = mass of substance
c = specific heat capacity
T2 = final temperature
T1 = initial temperature
**note: if Q is (-), heat is released and if (+), heat is absorbed

now we can only apply this to substances that did not change its phase, but in the problem, we see that phase change occurs. from solid lead->liquid lead.
thus we need another data called Latent Heat of Fusion to calculate for the heat required to change its phase:
H = m(Lf)

where
m = mass
Lf = Latent Heat of Fusion (fusion means melting)

substituting:
Q = mc(T2-T1)
Q = 250*(0.028)*(328-20)
Q = 2156 cal
*note that is is only for the temp change,, it's phase is still solid.
now to change its phase,
H = m*Lf
H = 250*5.5
H = 1375 cal

thus the total heat (Q,total) needed is
Q,total = Q + H = 2156 + 1375
Q,total = 3531 calories

hope this helps~ :)

To calculate the amount of heat required to melt the lead, we need to consider two factors: the heat required to raise the temperature of the lead from 20°C to its melting point (328°C) and the heat required for the actual phase change (melting).

First, let's calculate the heat required to raise the temperature of the lead from 20°C to the melting point:

Heat = mass × specific heat × temperature difference

The mass is given as 250 kg.
The specific heat of lead is given as 0.028 kcal/kg°C.
The temperature difference is (melting point - initial temperature) = (328°C - 20°C) = 308°C.

Heat = 250 kg × 0.028 kcal/kg°C × 308°C

Next, let's calculate the heat required for the phase change (melting):

Heat for melting = mass × heat fusion

The mass is given as 250 kg.
The heat fusion is given as 5.5 kcal/kg.

Heat for melting = 250 kg × 5.5 kcal/kg

Finally, to find the total heat required, we sum up both the heat for raising the temperature and the heat for melting:

Total heat = Heat for raising temperature + Heat for melting

Total heat = (250 kg × 0.028 kcal/kg°C × 308°C) + (250 kg × 5.5 kcal/kg)

Now we can compute the total heat required.

To calculate the heat required to melt a sample of lead, we need to consider two steps: heating the lead from 20°C to its melting point, and then melting the lead at its melting point.

Step 1: Heating the lead from 20°C to 328°C
To calculate the heat required to heat the lead from 20°C to 328°C, we use the equation:

Heat = Mass * Specific Heat * Temperature Change

Given:
Mass of lead (m) = 250 kg
Specific heat (c) = 0.028 kcal/kg°C
Initial temperature (T1) = 20°C
Final temperature (T2) = 328°C

Substituting the values into the equation, we get:

Heat = 250 kg * 0.028 kcal/kg°C * (328°C - 20°C)

Step 2: Melting the lead at its melting point
To calculate the heat required to melt the lead at its melting point, we use the equation:

Heat = Mass * Heat Fusion

Given:
Mass of lead (m) = 250 kg
Heat fusion (Hf) = 5.5 kcal/kg

Substituting the values into the equation, we get:

Heat = 250 kg * 5.5 kcal/kg

Now, we can calculate the total heat required by adding the heat from step 1 and step 2:

Total Heat = Heat (Step 1) + Heat (Step 2)

Therefore,
Total Heat = (250 kg * 0.028 kcal/kg°C * (328°C - 20°C)) + (250 kg * 5.5 kcal/kg)

Simplifying this equation will give you the total heat required to melt the 250 kg sample of lead from a temperature of 20°C to its melting point of 328°C.