The amount of heat (in calories) required to convert 5g of ice at `0^(@)C` to steam at `100^@C` is
`[L_("fusion") = 80 cal g^(-1), L_("vaporization") = 540 cal g^(-1)]`

Options

A. 3100
B. 3200
C. 3600
D. 4200

Answer

To solve the problem of calculating the total heat required to convert 5 grams of ice at \(0^\circ C\) to steam at \(100^\circ C\), we will follow these steps:

### Step 1: Convert Ice to Water at \(0^\circ C\)
First, we need to convert the ice at \(0^\circ C\) to water at \(0^\circ C\). The heat required for this process is given by the formula:
\[ Q_1 = m \cdot L_{fusion} \]
Where:
- \(m = 5 \, \text{g}\) (mass of ice)
- \(L_{fusion} = 80 \, \text{cal/g}\) (latent heat of fusion)

Calculating \(Q_1\):
\[ Q_1 = 5 \, \text{g} \cdot 80 \, \text{cal/g} = 400 \, \text{cal} \]

### Step 2: Heat Water from \(0^\circ C\) to \(100^\circ C\)
Next, we need to heat the water from \(0^\circ C\) to \(100^\circ C\). The heat required for this process is given by:
\[ Q_2 = m \cdot c \cdot \Delta T \]
Where:
- \(c = 1 \, \text{cal/g}^\circ C\) (specific heat of water)
- \(\Delta T = 100^\circ C - 0^\circ C = 100^\circ C\)

Calculating \(Q_2\):
\[ Q_2 = 5 \, \text{g} \cdot 1 \, \text{cal/g}^\circ C \cdot 100^\circ C = 500 \, \text{cal} \]

### Step 3: Convert Water to Steam at \(100^\circ C\)
Finally, we need to convert the water at \(100^\circ C\) to steam at \(100^\circ C\). The heat required for this process is given by:
\[ Q_3 = m \cdot L_{vaporization} \]
Where:
- \(L_{vaporization} = 540 \, \text{cal/g}\) (latent heat of vaporization)

Calculating \(Q_3\):
\[ Q_3 = 5 \, \text{g} \cdot 540 \, \text{cal/g} = 2700 \, \text{cal} \]

### Step 4: Total Heat Required
Now, we can find the total heat required by summing all the heat quantities calculated:
\[ Q_{total} = Q_1 + Q_2 + Q_3 \]
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 5 grams of ice at \(0^\circ C\) to steam at \(100^\circ C\) is **3600 calories**.