A sample of O2 is at a pressure of 1 atm when the volume is 100ml and its temperature is 27C .what will be the temperature of the gas if the pressure becomes 2 atm and volume remains 100 ml.

Explanation

To solve the problem, we will use the relationship between pressure, volume, and temperature for a gas. Since the volume remains constant, we can use the formula derived from the ideal gas law, which states that pressure is directly proportional to temperature when volume is constant.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Initial Pressure (P1) = 1 atm
- Final Pressure (P2) = 2 atm
- Initial Temperature (T1) = 27°C

2. **Convert Temperature from Celsius to Kelvin:**
- To convert Celsius to Kelvin, use the formula:
\[ T(K) = T(°C) + 273 \]
- Therefore,
\[ T1 = 27 + 273 = 300 \text{ K} \]

3. **Use the Formula for Constant Volume:**
- Since the volume is constant, we can use the relation:
\[ \frac{P1}{T1} = \frac{P2}{T2} \]
- Rearranging this gives:
\[ T2 = \frac{P2}{P1} \times T1 \]

4. **Substitute the Known Values:**
- Substitute P1, P2, and T1 into the equation:
\[ T2 = \frac{2 \text{ atm}}{1 \text{ atm}} \times 300 \text{ K} \]
- This simplifies to:
\[ T2 = 2 \times 300 = 600 \text{ K} \]

5. **Convert Temperature Back to Celsius:**
- To convert from Kelvin back to Celsius, use the formula:
\[ T(°C) = T(K) - 273 \]
- Therefore,
\[ T2 = 600 - 273 = 327 \text{ °C} \]

### Final Answer:
The temperature of the gas when the pressure becomes 2 atm and the volume remains 100 ml is **327 °C**.

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