The resistance of the wire in the platinum resistance thermometer at ice point is `5Omega` and at steam point is `5.25Omega`. When the thermometer is inserted in an unknown hot bath its resistance is found to be `5.5Omega`. The temperature of the hot bath is

Options

A. `100^(@)C`
B. `200^(@)C`
C. `300^(@)C`
D. `350^(@)C`

Explanation

To find the temperature of the hot bath using the resistance of the platinum resistance thermometer, we can use the formula that relates resistance and temperature. The formula is given by:

\[ R_T = R_0 (1 + \alpha T) \]

Where:
- \( R_T \) is the resistance at temperature \( T \).
- \( R_0 \) is the resistance at the ice point (0°C).
- \( \alpha \) is the temperature coefficient of resistance.
- \( T \) is the temperature in degrees Celsius.

### Step-by-Step Solution:

1. **Identify Known Values:**
- Resistance at ice point, \( R_0 = 5 \, \Omega \) (at 0°C)
- Resistance at steam point, \( R_{100} = 5.25 \, \Omega \) (at 100°C)
- Resistance in the hot bath, \( R_T = 5.5 \, \Omega \)

2. **Calculate the Temperature Coefficient of Resistance (\( \alpha \)):**
- We know that the resistance changes from \( R_0 \) to \( R_{100} \) as the temperature changes from 0°C to 100°C.
- Using the formula for resistance at steam point:
\[ R_{100} = R_0 (1 + \alpha \cdot 100) \]
- Substitute the known values:
\[ 5.25 = 5 (1 + 100\alpha) \]
- Simplifying gives:
\[ 1 + 100\alpha = \frac{5.25}{5} = 1.05 \]
- Thus:
\[ 100\alpha = 1.05 - 1 = 0.05 \]
\[ \alpha = \frac{0.05}{100} = 0.0005 \, \text{°C}^{-1} \]

3. **Use the Resistance in the Hot Bath to Find Temperature:**
- Now we can use the resistance in the hot bath to find the temperature:
\[ R_T = R_0 (1 + \alpha T) \]
- Substitute \( R_T = 5.5 \, \Omega \), \( R_0 = 5 \, \Omega \), and \( \alpha = 0.0005 \):
\[ 5.5 = 5 (1 + 0.0005 T) \]
- Dividing both sides by 5:
\[ 1.1 = 1 + 0.0005 T \]
- Rearranging gives:
\[ 0.1 = 0.0005 T \]
- Solving for \( T \):
\[ T = \frac{0.1}{0.0005} = 200 \, \text{°C} \]

### Final Answer:
The temperature of the hot bath is **200°C**.