A vessel contains 1 mole of `O_2` at a temperature T. The pressure of gas is P. An identical vessel containing 1 mole of the gas at a temperature 2T has pressure of -

Options

A. P
B. 2P
C. 3P
D. 4P

Answer

To solve the problem, we need to use the relationship between pressure, volume, temperature, and the number of moles of a gas, which is described by the Ideal Gas Law and Kinetic Theory of Gases.

### Step-by-Step Solution:

1. **Understand the Problem**: We have two identical vessels containing 1 mole of `O2` gas each. The first vessel has a temperature `T` and pressure `P`. The second vessel has a temperature `2T`, and we need to find its pressure.

2. **Identify the Relevant Equation**: According to the Ideal Gas Law, for a given number of moles of gas at constant volume, the pressure is directly proportional to the temperature:
\[ P \propto T \]
This means that if the temperature changes, the pressure will change proportionally.

3. **Set Up the Proportional Relationship**: Let the pressure in the second vessel (at temperature `2T`) be `P2`. From the relationship established, we can write:
\[ \frac{P2}{P} = \frac{2T}{T} \]

4. **Simplify the Equation**: The equation simplifies to:
\[ \frac{P2}{P} = 2 \]

5. **Solve for P2**: Rearranging gives us:
\[ P2 = 2P \]

6. **Conclusion**: Therefore, the pressure in the second vessel at temperature `2T` is `2P`.

### Final Answer:
The pressure in the second vessel is `2P`.

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