The pressure of an ideal gas is directly proportional to

Options

A. total kinetic energy
B. translational kinetic energy
C. rotational kinetic energy
D. vibrational kinetic energy

Explanation

To solve the question regarding the relationship between the pressure of an ideal gas and its kinetic energy, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Ideal Gas Law**:
The ideal gas law states that \( PV = nRT \), where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the universal gas constant, and \( T \) is the temperature in Kelvin.

2. **Kinetic Theory of Gases**:
According to the kinetic theory of gases, the pressure exerted by an ideal gas is related to the average kinetic energy of the gas molecules. The total kinetic energy (KE) of the gas can be expressed as:
\[ KE = \frac{3}{2} nRT \]
This shows that the total kinetic energy is directly proportional to the temperature of the gas.

3. **Relating Pressure and Kinetic Energy**:
From the ideal gas law, we can express the temperature \( T \) in terms of pressure and volume:
\[ T = \frac{PV}{nR} \]
Substituting this expression for \( T \) back into the kinetic energy equation gives:
\[ KE = \frac{3}{2} nR \left(\frac{PV}{nR}\right) = \frac{3}{2} PV \]
This indicates that the total kinetic energy is directly proportional to the product of pressure and volume.

4. **Conclusion**:
Since we have established that the total kinetic energy of the gas is proportional to \( PV \), and pressure \( P \) is part of this relationship, we can conclude that the pressure of an ideal gas is directly proportional to its total kinetic energy.

### Final Answer:
The pressure of an ideal gas is directly proportional to the total kinetic energy.