When a gas enclosed in a closed vessel was heated so as to increase its temperature by `5^(@)C`, its pressure was seen to have increased by 1%. The initial temperature of the gas was nearly

Options

A. `500^(@)C`
B. `227^(@)C`
C. `273^(@)C`
D. `150^(@)C`

Explanation

To solve the problem, we will use the ideal gas law and the relationship between temperature and pressure changes.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Change in temperature, \( \Delta T = 5^\circ C \)
- Change in pressure, \( \Delta P = 1\% \) of initial pressure \( P \)

2. **Convert the Percentage Change in Pressure:**
- Since \( \Delta P = 1\% \), we can express this as:
\[ \Delta P = 0.01 P \]

3. **Use the Ideal Gas Law Relation:**
- According to the ideal gas law, for a constant volume, the relationship between the change in pressure and change in temperature can be expressed as:
\[ \frac{\Delta P}{P} = \frac{\Delta T}{T} \]
- Here, \( T \) is the initial temperature in Kelvin.

4. **Substitute the Known Values:**
- We can substitute the values we have into the equation:
\[ \frac{0.01 P}{P} = \frac{5}{T} \]
- This simplifies to:
\[ 0.01 = \frac{5}{T} \]

5. **Rearranging the Equation:**
- Rearranging gives:
\[ T = \frac{5}{0.01} = 500 \text{ K} \]

6. **Convert Kelvin to Celsius:**
- To find the initial temperature in degrees Celsius, we use the conversion:
\[ T_{C} = T_{K} - 273 \]
- Substituting the value we found:
\[ T_{C} = 500 - 273 = 227^\circ C \]

### Final Answer:
The initial temperature of the gas was nearly \( 227^\circ C \).

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