Two gases A and B having the same pressure P, volume V and temperature T are mixed. If mixture has volume and temperature as V and T respectively, then the pressure of the mixture will be

Options

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

Answer

To solve the problem of finding the pressure of the mixture of two gases A and B, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- Both gases A and B have the same pressure \( P \), volume \( V \), and temperature \( T \).
- The mixture of gases A and B also has the same volume \( V \) and temperature \( T \).

2. **Use the Ideal Gas Law**:
- The ideal gas law is given by the equation:
\[ PV = nRT \]
- Here, \( n \) is the number of moles, \( R \) is the universal gas constant, and \( T \) is the temperature.

3. **Calculate the Number of Moles for Each Gas**:
- For gas A:
\[ n_A = \frac{PV}{RT} \]
- For gas B (since it has the same conditions):
\[ n_B = \frac{PV}{RT} \]
- Therefore, the number of moles for both gases A and B is the same, \( n_A = n_B = n \).

4. **Calculate the Total Number of Moles in the Mixture**:
- The total number of moles in the mixture (A + B) is:
\[ n_{\text{total}} = n_A + n_B = n + n = 2n \]

5. **Apply the Ideal Gas Law to the Mixture**:
- For the mixture, using the ideal gas law:
\[ P'V = n_{\text{total}}RT \]
- Substituting \( n_{\text{total}} = 2n \):
\[ P'V = (2n)RT \]

6. **Substitute the Value of \( n \)**:
- From earlier, we know \( n = \frac{PV}{RT} \), so substituting this into the equation gives:
\[ P'V = 2 \left(\frac{PV}{RT}\right) RT \]

7. **Simplify the Equation**:
- The \( RT \) terms cancel out:
\[ P'V = 2PV \]
- Now, divide both sides by \( V \):
\[ P' = 2P \]

8. **Conclusion**:
- The pressure of the mixture \( P' \) is:
\[ P' = 2P \]

### Final Answer:
The pressure of the mixture will be \( 2P \).

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