Heat required to convert 1 g of ice at `0^(@)C` into steam at `100 ^(@)C` is

Options

A. 100 cal
B. `0.01 cal//^(@)C`
C. 720 cal
D. 1 kilocal

Explanation

To find the heat required to convert 1 g of ice at \(0^\circ C\) into steam at \(100^\circ C\), we need to consider the different stages of this phase change. The process involves three main steps:

1. **Melting the ice to water at \(0^\circ C\)**.
2. **Heating the water from \(0^\circ C\) to \(100^\circ C\)**.
3. **Vaporizing the water to steam at \(100^\circ C\)**.

Let's calculate the heat required for each step:

### Step 1: Melting Ice to Water
The heat required to melt ice is given by the formula:
\[ Q_1 = m \cdot L_f \]
where:
- \(m\) = mass of ice = 1 g
- \(L_f\) = latent heat of fusion of ice = 80 cal/g

Calculating \(Q_1\):
\[ Q_1 = 1 \, \text{g} \cdot 80 \, \text{cal/g} = 80 \, \text{cal} \]

### Step 2: Heating Water from \(0^\circ C\) to \(100^\circ C\)
The heat required to raise the temperature of water is given by:
\[ Q_2 = m \cdot c \cdot \Delta T \]
where:
- \(c\) = specific heat capacity of water = 1 cal/g°C
- \(\Delta T\) = change in temperature = \(100^\circ C - 0^\circ C = 100^\circ C\)

Calculating \(Q_2\):
\[ Q_2 = 1 \, \text{g} \cdot 1 \, \text{cal/g°C} \cdot 100 \, \text{°C} = 100 \, \text{cal} \]

### Step 3: Vaporizing Water to Steam
The heat required to vaporize water is given by:
\[ Q_3 = m \cdot L_v \]
where:
- \(L_v\) = latent heat of vaporization of water = 540 cal/g

Calculating \(Q_3\):
\[ Q_3 = 1 \, \text{g} \cdot 540 \, \text{cal/g} = 540 \, \text{cal} \]

### Total Heat Required
Now, we can find the total heat required by summing up all the heat calculated in the three steps:
\[ Q_{total} = Q_1 + Q_2 + Q_3 \]
\[ Q_{total} = 80 \, \text{cal} + 100 \, \text{cal} + 540 \, \text{cal} = 720 \, \text{cal} \]

Thus, the total heat required to convert 1 g of ice at \(0^\circ C\) into steam at \(100^\circ C\) is **720 calories**.

### Final Answer
The heat required to convert 1 g of ice at \(0^\circ C\) into steam at \(100^\circ C\) is **720 calories**.

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