To solve the problem of calculating the total amount of heat required to convert 5g of ice at \(0^\circ C\) to steam at \(100^\circ C\), we will break the process down into three main steps: melting the ice, heating the water, and vaporizing the water.
### Step 1: Calculate the heat required to melt the ice
The heat required to melt ice (latent heat of fusion) can be calculated using the formula:
\[
Q_1 = m \cdot L_{fusion}
\]
Where:
- \(Q_1\) = heat required to melt the ice
- \(m\) = mass of ice = 5 g
- \(L_{fusion}\) = latent heat of fusion = 80 cal/g
Substituting the values:
\[
Q_1 = 5 \, \text{g} \cdot 80 \, \text{cal/g} = 400 \, \text{cal}
\]
### Step 2: Calculate the heat required to raise the temperature of water from \(0^\circ C\) to \(100^\circ C\)
The heat required to raise the temperature can be calculated using the formula:
\[
Q_2 = m \cdot c \cdot \Delta T
\]
Where:
- \(Q_2\) = heat required to raise the temperature
- \(c\) = specific heat of water = 1 cal/g°C
- \(\Delta T\) = change in temperature = \(100^\circ C - 0^\circ C = 100^\circ C\)
Substituting the values:
\[
Q_2 = 5 \, \text{g} \cdot 1 \, \text{cal/g°C} \cdot 100 \, \text{°C} = 500 \, \text{cal}
\]
### Step 3: Calculate the heat required to vaporize the water
The heat required to vaporize water (latent heat of vaporization) can be calculated using the formula:
\[
Q_3 = m \cdot L_{vaporization}
\]
Where:
- \(Q_3\) = heat required to vaporize the water
- \(L_{vaporization}\) = latent heat of vaporization = 540 cal/g
Substituting the values:
\[
Q_3 = 5 \, \text{g} \cdot 540 \, \text{cal/g} = 2700 \, \text{cal}
\]
### Step 4: Calculate the total heat required
Now, we can find the total heat required by adding all three heat quantities:
\[
Q_{total} = Q_1 + Q_2 + Q_3
\]
Substituting the values:
\[
Q_{total} = 400 \, \text{cal} + 500 \, \text{cal} + 2700 \, \text{cal} = 3600 \, \text{cal}
\]
Thus, the total amount of heat required to convert 5g of ice at \(0^\circ C\) to steam at \(100^\circ C\) is **3600 calories**.
