| Pressure | Temperature | Volume | msv | |
| Final | 0.37 | 306 | 72.5 | 2752 |
| Initial | 0.37 | 306 | 72.5 | 2752 |
| D | 0 | 0 | 0 | 0 |
No heat was gained or lost by the ideal monatomic gas and no work was done on or by the gas. Therefore, there was no change in the kinetic energy of the gas and no change in the pressure, temperature, or volume of the gas.
| Pressure | Temperature | Volume | msv | |
| Final | 0.64 | 519 | 72.5 | 4600 |
| Initial | 0.36 | 297 | 72.5 | 2700 |
| D | 0.28 | 222 | 0 | 1900 |
The ideal monatomic gas occupied a container with a fixed volume and absorbed heat (energy) from a "hot" bath. The pressure, temperature, and the mean kinetic energy of the gas increased.
When the gaseous atoms collide with the hot cylinder wall, they gain kinetic energy. As the mean kinetic energy ,
,of the atoms increases, the mean square velocity, 
, increases and hence the pressure, 
, and the temperature , 
, increase in the constant volume process. In this constant volume process all of the heat (energy) absorbed from the "hot" bath is used to increase the kinetic energy of the gas.
| Pressure | Temperature | Volume | msv | |
| Final | 0.36 | 240 | 59.5 | 2231 |
| Initial | 0.36 | 297 | 72.5 | 2655 |
| D | 0 | -57 | -13 | -424 |
The ideal monatomic gas was placed in a cylinder with a movable piston and cooled. The volume, temperature, and mean kinetic energy of the gas decreased. The pressure of the gas remained constant.
The gaseous atoms lose kinetic energy when they collide with the cold cylinder wall. As the mean kinetic energy,
, of the atoms decreases, the mean square velocity and hence the temperature decrease. The piston exerts a constant pressure on the gas. The pressure exerted on the piston by the gas decreases as the mean kinetic energy of the atoms decreases. Since the pressure of piston is greater than the pressure exerted by the gas, the gas is compressed and the volume of the gas decreases until the pressure of the gas again equals the pressure of the piston. As the piston moves in and collides with gaseous atoms, momentum is transferred from the piston to the atoms and the kinetic energy of the atoms increases. This additional kinetic energy is eventually lost to the "cold" bath when the atoms collide with the cylinder wall. In this constant pressure process some of the kinetic energy of the gas is lost to the "cold" bath and the work done on the gas is lost as heat to the "cold" bath.
| Pressure | Temperature | Volume | msv | |
| Final | 0.52 | 346 | 59.5 | 3100 |
| Initial | 0.37 | 306 | 72.5 | 2752 |
| D | 0.15 | 40 | -13 | 348 |
In this process the cylinder is covered with insulation to prohibit the transfer of energy (heat) from the surroundings to the gas and from the gas to the surroundings. The pressure exerted by the piston on the gas is slowly increased. The gas was compressed and the pressure, temperature, and mean square velocity of the gas increased.
Since the pressure exerted on the gas by the piston is greater than the pressure exerted on the piston by the gas, the piston moves in and the gas is compressed. As the piston moves in, it collides with gaseous atoms and momentum is transferred from the piston to the atoms. The kinetic energy of the atoms increases. As the mean kinetic energy,
, of the atoms increases, the mean square velocity, , increases and hence the temperature, , increases. Both the increase in the mean square velocity and the decrease in the volume of the gas contribute to the increase in the pressure, , of the gas. In this adiabatic process the work done on the gas increases the kinetic energy of the gas.
| Pressure | Temperature | Volume | msv | |
| Final | 0.47 | 316 | 59.5 | 2836 |
| Initial | 0.39 | 316 | 72.5 | 2837 |
| D | 0.08 | 0 | -13 | 1 |
In this process the cylinder was placed in a constant temperature bath and the pressure exerted by the piston on the gas was increased slowly. As the gas was compressed, the pressure of the gas increased. The constant temperature bath ensures that the temperature of the gas remains constant during the process. Hence, the temperature and mean square velocity remained effectively constant.
As the pressure exerted on the gas by the piston increases, the piston moves in and collides with gaseous atoms. Momentum is transferred from the piston to the atoms and the kinetic energy of the atoms increases. There is a momentary increase in the mean kinetic energy of the atoms and the temperature of the gas. When warmer atoms collide with the cooler cylinder wall, the kinetic energy of the atoms decreases. In this instance there is a momentary decrease in the mean kinetic energy of the atoms and the temperature of the gas. Thousands of these events occur in the time interval that it takes to measure the temperature and thus the measured temperature is an average temperature. In this process the average temperature and the mean square velocity remain constant from one time interval to the next. The increase in the pressure of the gas is a result of the decrease in the volume occupied by the gas.
In this constant temperature process the work done on the gas is lost as heat to the constant temperature bath and the mean kinetic energy of the atoms remains constant.