The specfic heat of iron is 0.11cal/g C. The heat of fusion of iron, the heat required to convert iron from a solid to liquid at its melting point, is 63.7cal/g. Iron melts at 1530 C. How much heat must be added to 2g of iron at 25c to completely melt it?
q1 = heat added to raise T of Fe from 25C to 1530 C.
q1 = mass Fe x specific heat Fe x (Tfinal-Tinitial)
q2 = heat to melt Fe at 1530C.
q2 = mass Fe x heat fusion/g
Total Q = q1 + q2
458.5cal
To calculate the total amount of heat required to melt the iron, we need to consider two steps: first, raising the temperature of the iron from 25°C to its melting point, and second, melting the iron at its melting point.
Step 1: Heating the iron from 25°C to its melting point.
The specific heat formula is Q = mcΔT, where Q is the heat energy, m is the mass, c is the specific heat, and ΔT is the temperature change.
Q1 = (mass) × (specific heat) × (temperature change)
= (2g) × (0.11 cal/g°C) × (1530°C - 25°C)
= 2 × 0.11 × 1505
= 331.1 cal
Step 2: Melting the iron at its melting point.
The heat of fusion is the amount of heat required to convert 1 gram of a substance from a solid to a liquid at its melting point.
Q2 = (mass) × (heat of fusion)
= (2g) × (63.7 cal/g)
= 127.4 cal
The total heat required to completely melt 2 grams of iron is the sum of Q1 and Q2:
Total heat = Q1 + Q2
= 331.1 cal + 127.4 cal
= 458.5 cal
Therefore, 458.5 calories of heat must be added to 2 grams of iron at 25°C to completely melt it.
To determine the amount of heat required to completely melt 2g of iron, we need to consider two factors: the heat required to raise the temperature of the iron from 25°C to its melting point (1530°C) and the heat of fusion required to convert the solid iron into liquid iron at its melting point.
To calculate the heat required to raise the temperature of the iron, we will use the specific heat formula:
Q = m * c * ΔT
Where:
Q is the heat energy (in calories)
m is the mass of the substance (in grams)
c is the specific heat capacity (in cal/g°C)
ΔT is the change in temperature (in °C)
Given:
m = 2g (mass of iron)
c = 0.11 cal/g°C (specific heat of iron)
ΔT = 1530°C - 25°C = 1505°C
Plugging the values into the formula:
Q1 = (2g) * (0.11 cal/g°C) * (1505°C)
Q1 = 331.1 cal
So, the heat required to raise the temperature of the iron from 25°C to its melting point is 331.1 calories.
Next, we need to calculate the heat of fusion required to convert the solid iron into liquid iron at its melting point.
Given:
m = 2g (mass of iron)
Heat of fusion of iron = 63.7 cal/g
Q2 = (2g) * (63.7 cal/g)
Q2 = 127.4 cal
So, the heat of fusion required to melt 2g of iron at its melting point is 127.4 calories.
To find the total heat required to completely melt the iron, we add the two values calculated above:
Total heat required = Q1 + Q2
Total heat required = 331.1 cal + 127.4 cal
Total heat required = 458.5 cal
Therefore, to completely melt 2g of iron at 25°C, you would need to add 458.5 calories of heat.