If we increase temperature of a gas sample, which of the following is true?

Options

A. K.E. of gas sample decrease
B. Average speed remains constant
C. Average momentum remains constant
D. P.E. of gas sample increases

Explanation

To determine the effect of increasing the temperature of a gas sample, we need to analyze the properties of gas molecules and how they relate to temperature. Let's break down the solution step by step:

### Step 1: Understand the relationship between temperature and kinetic energy
- The temperature of a gas is directly related to the average kinetic energy of its molecules. As the temperature increases, the average kinetic energy of the gas molecules also increases.

### Step 2: Analyze the average speed of gas molecules
- The average speed of gas molecules can be expressed using the formula:
\[ v_{avg} = \sqrt{\frac{3kT}{m}} \]
where \( k \) is the Boltzmann constant, \( T \) is the absolute temperature, and \( m \) is the mass of a gas molecule.
- From this equation, we can see that as the temperature \( T \) increases, the average speed \( v_{avg} \) also increases.

### Step 3: Consider the average momentum of gas molecules
- The momentum of a gas molecule is given by \( p = mv \), where \( m \) is the mass and \( v \) is the velocity of the molecule.
- Although the individual velocities of the molecules change with temperature, the average momentum of the gas molecules can remain constant if the distribution of velocities is isotropic (equal in all directions).

### Step 4: Conclusion
- When the temperature of a gas sample is increased, the average kinetic energy and average speed of the gas molecules increase. However, the average momentum remains constant because the velocities of the molecules are independent of temperature and are distributed uniformly in all directions.

### Final Answer
- Therefore, the correct statement is: **Average momentum remains constant.**

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