So for the gas laws variables, I was confused about what would happen if different variables were changed.

1) If a sample of gas is heated in a rigid container of constant volume and constant amount of gas what would happen to the average distance between the gas particles and what would happen to the density of the gas? In both of these cases would the variable increase, decrease or stay the same?

2) In these cases would the variable increase, decrease or stay the same? If a sample of gas is in a cylinder with a moveable piston and the gas volume is reduced from 1.0L to 0.5L at a constant temperature and constant amount of gas what would happen to the average speed of the gas particles and what would happen to the average distance between the gas particles? Also, what would happen to the average kinetic energy? Would the average kinetic energy be the same because it has the same temperature?

3) If a sample of gas is in a rigid container of constant volume and an additional gas is injected into the container at a constant temperature what would happen to the average kinetic energy and the average speed of the gas particles? In the answer key, it says both of these will stay the same but I don't understand why.

4) If a sample of gas is placed in an expandable balloon and the temperature is reduced from 300k to 200k while maintaining a constant pressure and a constant amount of gas what would happen to the average kinetic energy, average speed of the particles, and the number of collisions within the gas. In the answer key, it says the number of collisions will stay the same shouldn't it decrease?

5) Finally I was wondering how temperature relates to kinetic energy and the average speed of the particles when talking about gases generally.

Hey Dr.Sharma, I just wanted to mention that this is Aiswharya from your class on Saturdays and Tuesdays India time.

Quote from: Aiswharyaa Nagarajan on October 22, 2024, 01:05:18 AMHey Dr.Sharma, I just wanted to mention that this is Aiswharya from your class on Saturdays and Tuesdays India time.

Hi
There was big break down of internet that was the reason could not answer the question.
Here is the answer of each question separately.

1) If a sample of gas is heated in a rigid container of constant volume and constant amount of gas what would happen to the average distance between the gas particles and what would happen to the density of the gas? In both of these cases would the variable increase, decrease or stay the same?

Density = mass and volume
Mass and volume are kept constant as mentioned in the question so density stays the same.With increase in temperature KE increases ,no of collisions increases and hence pressure increases.

2) In these cases would the variable increase, decrease or stay the same? If a sample of gas is in a cylinder with a moveable piston and the gas volume is reduced from 1.0L to 0.5L at a constant temperature and constant amount of gas what would happen to the average speed of the gas particles and what would happen to the average distance between the gas particles? Also, what would happen to the average kinetic energy? Would the average kinetic energy be the same because it has the same temperature?

When temperature is constant, the kinetic energy (KE) of the particles remains the same, meaning their average speed does not change.
However, if the volume of the gas decreases, the particles are forced closer together, reducing the average distance between them.
As a result, the frequency of collisions with the walls of the container increases, leading to a rise in pressure.

If a sample of gas is in a rigid container of constant volume and an additional gas is injected into the container at a constant temperature what would happen to the average kinetic energy and the average speed of the gas particles? In the answer key, it says both of these will stay the same but I don't understand why.


The average kinetic energy (KE) and average speed of gas particles depend on temperature. When the temperature is constant, both KE and average speed remain unchanged.

The relationship can be expressed as:

KE=  3/2 RT
KE = 1/2 M u²

In this scenario, if the amount of gas increases while keeping the volume and temperature constant, pressure will rise due to an increase in the number of collisions per unit area. However, the average kinetic energy and average speed of the gas particles will remain constant since temperature is unchanged.

4) If a sample of gas is placed in an expandable balloon and the temperature is reduced from 300k to 200k while maintaining a constant pressure and a constant amount of gas what would happen to the average kinetic energy, average speed of the particles, and the number of collisions within the gas. In the answer key, it says the number of collisions will stay the same shouldn't it decrease?

In the balloon, as the temperature (T) decreases, the average kinetic energy (KE) and average speed of the gas particles also decrease, since KE is directly proportional to temperature.

Pressure is defined as the number of collisions per unit area.
While a decrease in temperature leads to fewer collisions as you mentioned, but the volume is also decreasing. This reduction in volume decreases the area available for collisions. As a result, the ratio of the number of collisions per unit area remains constant, keeping the pressure unchanged.

5) Finally I was wondering how temperature relates to kinetic energy and the average speed of the particles when talking about gases generally.
Average KE is directly proportional to Temperature and if T is not changing there is no change in averageKE
Ihe average kinetic energy (KE) of gas molecules is directly proportional to temperature. If the temperature (T) remains constant, there will be no change in the average KE.

For different gases with varying amounts, volumes, and pressures, but at the same temperature, the average KE of all gases will be the same.Check this equation to understand relation between average KE and average speed and temperature.
KE(avearge) = 3/2 RT - Here R is univerasl gas constant.
KE = 1/2 Mu²

The average KE is also directly proportional to the square of the root mean square (rms) velocity. If the average KE is not changing due to a constant temperature, the speed of the molecules will also remain unchanged.

However, if the temperature increases, the average KE will increase, causing the molecules to move at faster speeds.