Pressure remaining the constant, the volume of a given mass of an ideal gas increases for every degree centigrade rise in temperature by definite fraction of its volume at:

Options

A. `0^(@)C`
B. its critical temperature
C. absolute zero
D. its Boyle temperature

Explanation

To solve the question, we need to analyze the relationship between the volume of an ideal gas and its temperature while keeping the pressure constant. We will use the ideal gas law and concepts related to temperature in Celsius and Kelvin.

### Step-by-Step Solution:

1. **Understand the Ideal Gas Law**:
The ideal gas law is given by the equation:
\[ PV = nRT \]
where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles of gas, \( R \) is the ideal gas constant, and \( T \) is the absolute temperature in Kelvin.

2. **Constant Pressure Condition**:
Since the pressure \( P \) is constant and we are considering a given mass of gas (thus \( n \) is constant), we can rearrange the ideal gas law to express volume in terms of temperature:
\[ V = \frac{nRT}{P} \]
This shows that volume \( V \) is directly proportional to the absolute temperature \( T \).

3. **Temperature in Kelvin**:
The temperature in Kelvin is related to the Celsius temperature by the formula:
\[ T(K) = T(°C) + 273 \]
Thus, if we increase the temperature by 1°C, the corresponding increase in Kelvin is also 1K.

4. **Volume Change with Temperature**:
If we increase the temperature by 1°C (or 1K), the volume will increase by a certain fraction of its original volume. From the equation \( V = \frac{nR(T + 273)}{P} \), we can see that for every 1°C increase in temperature, the volume will increase by a definite fraction.

5. **Definite Fraction of Volume**:
The increase in volume for each degree Celsius can be expressed as:
\[ \Delta V = V(T + 1) - V(T) = \frac{nR(T + 1 + 273)}{P} - \frac{nR(T + 273)}{P} \]
Simplifying this gives:
\[ \Delta V = \frac{nR}{P} \]
This indicates that the volume increases by a constant amount for each degree increase in temperature.

6. **Conclusion**:
The question asks for the specific temperature condition under which this relationship holds true. The volume of a given mass of an ideal gas increases by a definite fraction of its volume at **0°C** (273 K) when pressure remains constant.

### Final Answer:
The volume of a given mass of an ideal gas increases for every degree centigrade rise in temperature by a definite fraction of its volume at **0°C**.

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