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 solve the question regarding the effect of increasing the temperature of a gas sample, we can analyze the properties of gases and how they relate to temperature changes.

### Step-by-Step Solution:

1. **Understanding Temperature and Kinetic Energy**:
- Temperature is a measure of the average kinetic energy of the particles in a gas. When the temperature of a gas increases, the kinetic energy of the gas particles also increases. This is due to the fact that temperature is directly proportional to the average kinetic energy of the molecules.

**Hint**: Recall that kinetic energy (KE) is related to temperature in gases.

2. **Kinetic Energy of Gas Sample**:
- Since increasing the temperature leads to an increase in the kinetic energy of the gas particles, the statement that "the kinetic energy of the gas sample decreases" is incorrect.

**Hint**: Think about the relationship between temperature and kinetic energy.

3. **Average Speed of Gas Particles**:
- As the temperature increases, the average speed of the gas particles also increases. Therefore, the statement that "the average speed remains constant" is also incorrect.

**Hint**: Consider how temperature affects the motion of gas particles.

4. **Average Momentum of Gas Particles**:
- The average momentum of gas particles is dependent on their mass and velocity. Since the mass of the gas particles remains constant and their velocity increases with temperature, the average momentum will also increase. Thus, the statement that "average momentum remains constant" is incorrect.

**Hint**: Remember that momentum is the product of mass and velocity.

5. **Potential Energy of Gas Sample**:
- In an ideal gas, the potential energy is generally considered negligible compared to kinetic energy. As the kinetic energy increases with temperature, the potential energy does not necessarily increase; it may even decrease in some contexts. Therefore, the statement that "the potential energy of the gas sample increases" is incorrect.

**Hint**: Reflect on the relationship between kinetic and potential energy in gases.

### Conclusion:
After analyzing all the options, we find that the correct interpretation is that increasing the temperature of a gas sample leads to an increase in kinetic energy and average speed, while average momentum also increases. The statements provided in the options are incorrect based on the principles of gas behavior.

**Final Answer**: None of the provided statements are true regarding the effects of increasing the temperature of a gas sample.