The temperature of a gas is increased by 1 °C. Then from the following statements pickout the correct one
1) The volume increases by 1/273 of its volume at 0°C at constant pressure
2) The pressure increases by 1/273 of its pressure at 0°C at constant volume
3) The volume decreases by 1/273 of its volume at 0°C
4) The pressure is doubled to its pressure at 0°C

Options

A. 1,3
B. 3,4
C. 1,2
D. 2,3

Answer

To solve the problem, we need to analyze the statements provided regarding the behavior of a gas when its temperature is increased by 1 °C. We will use the principles of gas laws, specifically Charles's Law and Gay-Lussac's Law.

### Step-by-Step Solution:

1. **Understanding the Context**:
- We are dealing with a gas whose temperature is increased by 1 °C. We need to determine the effects on volume and pressure based on the given statements.

2. **Applying Charles's Law**:
- Charles's Law states that at constant pressure, the volume of a gas is directly proportional to its absolute temperature (in Kelvin).
- The absolute temperature at 0 °C is 273 K. When the temperature is increased by 1 °C, the new temperature becomes 1 °C, which is 274 K.
- The change in volume can be expressed as:
\[ V_1 = V_0 \left(1 + \frac{1}{273}\right) \]
- This means the volume increases by \( \frac{1}{273} \) of its volume at 0 °C at constant pressure.
- **Conclusion**: Statement 1 is correct.

3. **Applying Gay-Lussac's Law**:
- Gay-Lussac's Law states that at constant volume, the pressure of a gas is directly proportional to its absolute temperature.
- The pressure at 0 °C is \( P_0 \) (at 273 K), and at 1 °C (274 K), the pressure can be expressed as:
\[ P_1 = P_0 \left(1 + \frac{1}{273}\right) \]
- This indicates that the pressure increases by \( \frac{1}{273} \) of its pressure at 0 °C at constant volume.
- **Conclusion**: Statement 2 is correct.

4. **Analyzing Statement 3**:
- The statement claims that the volume decreases by \( \frac{1}{273} \) of its volume at 0 °C. This is incorrect because, as we established from Charles's Law, the volume actually increases with an increase in temperature.
- **Conclusion**: Statement 3 is incorrect.

5. **Analyzing Statement 4**:
- The statement claims that the pressure is doubled to its pressure at 0 °C. This is also incorrect as we derived from Gay-Lussac's Law that the pressure increases but does not double with a 1 °C increase.
- **Conclusion**: Statement 4 is incorrect.

### Final Answer:
The correct statements are:
1) The volume increases by \( \frac{1}{273} \) of its volume at 0 °C at constant pressure.
2) The pressure increases by \( \frac{1}{273} \) of its pressure at 0 °C at constant volume.