The volume of a gas at `20^(@)C` is 100 cm 3 at normal pressure. If it is heated to `100^(@)C` , its volume becomes 125 cm 3 at the same pressure, then volume coefficient of the gas at normal pressure is

Options

A. `0.0015//^(@)C`
B. `0.0045//^(@)C`
C. `0.0025//^(@)C`
D. `0.0033//^(@)C`

Explanation

To find the volume coefficient of the gas at normal pressure, we can use the formula for volume expansion, which relates the change in volume to the change in temperature. The formula is given by:

\[ V = V_0 (1 + \gamma \Delta T) \]

Where:
- \( V \) is the final volume,
- \( V_0 \) is the initial volume,
- \( \gamma \) is the volume coefficient of the gas,
- \( \Delta T \) is the change in temperature.

### Step 1: Identify the initial and final conditions
- Initial volume \( V_0 = 100 \, \text{cm}^3 \) at \( T_0 = 20^\circ C \)
- Final volume \( V = 125 \, \text{cm}^3 \) at \( T = 100^\circ C \)

### Step 2: Calculate the change in temperature
\[ \Delta T = T - T_0 = 100^\circ C - 20^\circ C = 80^\circ C \]

### Step 3: Substitute the known values into the volume expansion formula
Using the volume expansion formula:
\[ 125 = 100 (1 + \gamma \cdot 80) \]

### Step 4: Simplify the equation
First, divide both sides by 100:
\[ 1.25 = 1 + 80\gamma \]

### Step 5: Rearrange to solve for \( \gamma \)
Subtract 1 from both sides:
\[ 0.25 = 80\gamma \]

Now, divide both sides by 80:
\[ \gamma = \frac{0.25}{80} = \frac{1}{320} \]

### Step 6: Convert to a decimal
Calculating the decimal value:
\[ \gamma = 0.003125 \, \text{per degree Celsius} \]

### Final Answer
Thus, the volume coefficient of the gas at normal pressure is:
\[ \gamma = 0.003125 \, \text{per degree Celsius} \]