Variation of volume with temperature was first studied by French chemist, Jacques Charles, in 1787 and then extended by another French chemist Joseph Gay-Lussac in 1802. For a fixed mass of a gas under isobaric condition, variation of volume V with temperature t°C is given by V = `V_(0)[l + alphat]` where `V_(0)` is the volume at 0°C, at constant pressure.
1 or every 1° change in temperature, the volume of the gas changes by............... of the volume at `0^(@)` C

Options

A. `1/273` unit
B. 1 unit
C. 273 unit
D. 22.4 unit

Answer

To solve the problem, we need to analyze the relationship between the volume of a gas and its temperature under isobaric conditions based on the equation provided.

### Step-by-Step Solution:

1. **Understand the Given Equation**:
The equation given is:
\[ V = V_0 [1 + \alpha t] \]
where \( V_0 \) is the volume at \( 0^\circ C \) and \( \alpha \) is the coefficient of volume expansion.

2. **Identify the Change in Temperature**:
We are interested in the change in volume for a temperature change of \( 1^\circ C \). Therefore, we will set \( t = 1 \).

3. **Substitute \( t = 1 \) into the Equation**:
Substitute \( t = 1 \) into the volume equation:
\[ V = V_0 [1 + \alpha \cdot 1] = V_0 [1 + \alpha] \]

4. **Calculate the Change in Volume**:
The change in volume (\( \Delta V \)) when the temperature increases by \( 1^\circ C \) can be calculated as:
\[ \Delta V = V - V_0 = V_0 [1 + \alpha] - V_0 = V_0 \alpha \]

5. **Determine the Coefficient of Volume Expansion**:
From the historical context provided, we know that the volume expansion coefficient \( \alpha \) for gases is approximately:
\[ \alpha = \frac{1}{273} \]

6. **Substitute \( \alpha \) into the Change in Volume**:
Now, substituting \( \alpha \) into the change in volume:
\[ \Delta V = V_0 \cdot \frac{1}{273} \]

7. **Express the Change in Volume as a Fraction of \( V_0 \)**:
The change in volume for a \( 1^\circ C \) increase in temperature is:
\[ \Delta V = \frac{V_0}{273} \]
This means that for every \( 1^\circ C \) change in temperature, the volume of the gas changes by \( \frac{1}{273} \) of the volume at \( 0^\circ C \).

### Final Answer:
For every \( 1^\circ C \) change in temperature, the volume of the gas changes by \( \frac{1}{273} \) of the volume at \( 0^\circ C \).

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