The parameter that remains the same for molecules of all gases at a given temperature is:

Options

A. speed
B. momentum
C. mass
D. kinetic energy

Answer

To solve the question, "The parameter that remains the same for molecules of all gases at a given temperature is:", we can follow these steps:

### Step 1: Understand the relationship between temperature and gas molecules
At a given temperature, gas molecules possess kinetic energy that is directly related to the temperature. The average kinetic energy of gas molecules can be expressed by the formula:
\[ KE = \frac{3}{2} k T \]
where \( k \) is the Boltzmann constant and \( T \) is the absolute temperature.

### Step 2: Identify the kinetic energy of gas molecules
Since the kinetic energy depends on temperature, we can conclude that at a constant temperature, the average kinetic energy of all gas molecules will be the same. This means that for all gases at a given temperature, the average kinetic energy is a constant value.

### Step 3: Relate kinetic energy to speed
The kinetic energy of a single molecule can also be expressed in terms of its mass and speed:
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is the mass of the molecule and \( v \) is its speed. Since the average kinetic energy is the same for all gases at a given temperature, we can infer that the average speed of gas molecules will also be related to this kinetic energy.

### Step 4: Analyze the implications for speed
If the average kinetic energy is the same, it implies that the average speed of the gas molecules will also be the same, considering that the mass of the molecules can vary. Therefore, the parameter that remains the same for molecules of all gases at a given temperature is the average speed.

### Step 5: Conclusion
Thus, the answer to the question is that the parameter that remains the same for molecules of all gases at a given temperature is **speed**.

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