540 calories of heat convert 1 cubic centimeter of water at `100^oC` into 1671 cubic centimeter of steam at `100^oC` at a pressure of one atmosphere. Then the work done against the atmospheric pressure is nearly

Answer

To solve the problem of calculating the work done against atmospheric pressure when converting 1 cubic centimeter of water at 100°C into 1671 cubic centimeters of steam at the same temperature, we can follow these steps:

### Step 1: Understand the Given Data
- Heat added (q) = 540 calories
- Initial volume of water (V1) = 1 cm³
- Final volume of steam (V2) = 1671 cm³
- Atmospheric pressure (P) = 1 atmosphere = 101325 Pa

### Step 2: Convert Volumes to SI Units
- Convert the volumes from cubic centimeters to cubic meters:
- V1 = 1 cm³ = 1 × 10⁻⁶ m³
- V2 = 1671 cm³ = 1671 × 10⁻⁶ m³

### Step 3: Calculate the Work Done
The work done against the atmospheric pressure (W) can be calculated using the formula:
\[ W = P \times (V2 - V1) \]

Substituting the values we have:
- \( V2 - V1 = (1671 × 10^{-6}) - (1 × 10^{-6}) = 1670 × 10^{-6} \) m³

Now substituting into the work formula:
\[ W = 101325 \, \text{Pa} \times (1670 × 10^{-6} \, \text{m}^3) \]

### Step 4: Perform the Calculation
Calculating the work done:
\[ W = 101325 \times 1670 \times 10^{-6} \]
\[ W = 169.21 \, \text{J} \]

### Final Answer
The work done against the atmospheric pressure is approximately **169.21 Joules**.

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