In a process, the pressure of a gas remains constant. If the temperature is doubles, then the change in the volume will be.

Options

A. `100 %`
B. `200 %`
C. `50 %`
D. `25 %`

Explanation

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the relationship between pressure, volume, and temperature.
According to the ideal gas law, the relationship between pressure (P), volume (V), and temperature (T) is given by the equation:
\[ PV = nRT \]
Where:
- \( P \) = pressure
- \( V \) = volume
- \( n \) = number of moles of gas
- \( R \) = universal gas constant
- \( T \) = absolute temperature in Kelvin

Since the pressure is constant, we can express the relationship between volume and temperature as:
\[ V \propto T \]
This means that volume is directly proportional to temperature when pressure is held constant.

### Step 2: Define the initial and final temperatures.
Let:
- \( T_1 \) = initial temperature
- \( T_2 \) = final temperature

According to the problem, the final temperature is double the initial temperature:
\[ T_2 = 2T_1 \]

### Step 3: Relate the initial and final volumes.
Since volume is directly proportional to temperature, we can express the initial and final volumes as:
- \( V_1 \) = initial volume
- \( V_2 \) = final volume

Using the proportionality:
\[ \frac{V_2}{V_1} = \frac{T_2}{T_1} \]

Substituting \( T_2 \):
\[ \frac{V_2}{V_1} = \frac{2T_1}{T_1} = 2 \]

This implies:
\[ V_2 = 2V_1 \]

### Step 4: Calculate the change in volume.
The change in volume (\( \Delta V \)) can be calculated as:
\[ \Delta V = V_2 - V_1 \]
Substituting \( V_2 \):
\[ \Delta V = 2V_1 - V_1 = V_1 \]

### Step 5: Calculate the percentage change in volume.
The percentage change in volume can be calculated using the formula:
\[ \text{Percentage Change} = \left( \frac{\Delta V}{V_1} \right) \times 100 \]
Substituting \( \Delta V \):
\[ \text{Percentage Change} = \left( \frac{V_1}{V_1} \right) \times 100 = 100\% \]

### Conclusion
The percentage change in volume when the temperature is doubled at constant pressure is **100%**.

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