At what temperature will the volume of a gas be twice the volume at `27^(0)C` at a given pressure.

Options

A. `327^(0)C`
B. `54^(0)C`
C. `127^(0)C`
D. `100^(0)C`

Explanation

To solve the problem of finding the temperature at which the volume of a gas is twice the volume at 27°C (given constant pressure), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: At constant pressure, the volume of a gas is directly proportional to its absolute temperature (in Kelvin). This relationship is expressed by Charles's Law:
\[ \frac{V_2}{V_1} = \frac{T_2}{T_1} \]

2. **Convert the Given Temperature**: The initial temperature \( T_1 \) is given as 27°C. We need to convert this temperature to Kelvin:
\[ T_1 = 27 + 273 = 300 \, \text{K} \]

3. **Define the Volumes**: Let the initial volume at 27°C be \( V_1 = V \). According to the problem, the final volume \( V_2 \) will be twice the initial volume:
\[ V_2 = 2V \]

4. **Set Up the Equation**: Using Charles's Law, we can set up the equation:
\[ \frac{V_2}{V_1} = \frac{T_2}{T_1} \]
Substituting the known values:
\[ \frac{2V}{V} = \frac{T_2}{300} \]

5. **Simplify the Equation**: This simplifies to:
\[ 2 = \frac{T_2}{300} \]

6. **Solve for \( T_2 \)**: To find \( T_2 \), we multiply both sides by 300:
\[ T_2 = 2 \times 300 = 600 \, \text{K} \]

7. **Convert Back to Celsius**: Finally, we convert the temperature back to Celsius:
\[ T_2 = 600 - 273 = 327 \, \text{°C} \]

### Final Answer:
The temperature at which the volume of the gas will be twice the volume at 27°C is **327°C**.

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