A constant pressure air thermometer gave a reading of 20 units of volume when immersedin ice and 22 units when immersed in hot water. The temperature of the hot water is

Options

A. `27.3^(@)C `
B. `112.07^(@)C`
C. `0^(@)C`
D. `273^(@)C`

Answer

To solve the problem, we will use Charles's Law, which states that the volume of a gas is directly proportional to its temperature when pressure is held constant.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Volume when immersed in ice (V1) = 20 units
- Volume when immersed in hot water (V2) = 22 units
- Temperature of ice (T1) = 0°C = 273 K (converted to Kelvin)

2. **Set Up the Relationship Using Charles's Law:**
According to Charles's Law:
\[ \frac{V1}{T1} = \frac{V2}{T2} \]
Here, we need to find T2 (the temperature of the hot water).

3. **Substitute Known Values into the Equation:**
\[ \frac{20}{273} = \frac{22}{T2} \]

4. **Cross-Multiply to Solve for T2:**
\[ 20 \cdot T2 = 22 \cdot 273 \]

5. **Calculate the Right Side:**
\[ 22 \cdot 273 = 6006 \]
So, we have:
\[ 20 \cdot T2 = 6006 \]

6. **Solve for T2:**
\[ T2 = \frac{6006}{20} = 300.3 \text{ K} \]

7. **Convert T2 from Kelvin to Celsius:**
\[ T2 = 300.3 - 273 = 27.3 \text{ °C} \]

### Final Answer:
The temperature of the hot water is **27.3 °C**.