In thermodynamics: Is Boyes Law P1V1 = P2V2 and Charles Law V1/T1 = V2/T2 Only true...

In thermodynamics:

Is Boyes Law P₁V₁ = P₂V₂

and Charles Law V₁/T₁ = V₂/T₂

Only true if the system is adiabatic? Or no heat transfer or work transfer or change in potential or kinetic energy?

Solutions

Expert Solution

In both cases, the system is not adiabatic, because in the Boyle Law temperature constant are considered and the Charles Law pressure constant are considered.

Boyle's law states that changing the volume of a gas at a constant temperature is inversely proportional to the pressure of the system. If the gas expands its pressure is reduced and if it is compressed it increases, so that work is produced, this is determined by the area under the curve of the next dimension P-V

When a gas is compressed its temperature increases, then to maintain thermal equilibrium, the heat transferred between the system and the environment will be equal to the work done by the system and the internal energy is equal to zero.

In the framework of the kinetic theory, the pressure of a gas is explained as the macroscopic result of the forces involved by the collisions of the gas molecules with the walls of the container. The pressure can therefore be defined by reference to the microscopic properties of the gas. Thus, when there is a change in pressure associated with a process of expansion or compression of a gas at a constant temperature, there are changes in the kinetic energy, at higher pressure the kinetic energy increases.

With respect to Charles's law, the change in volume as a function of temperature is related proportionally to constant pressure. If there is a volume change then the system performs work on the environment as shown in the following figure:

In an isobaric compression:

The temperature change is related to the internal energy change of the system:

, where Cv is calorific capacity to constant volume. Applying the first Thermodynamic Law the calor transferred in the process is:

The pressure of a gas depends directly on the molecular kinetic energy. The law of ideal gases allows us to ensure that the pressure is proportional to the absolute temperature. These two statements allow us to affirm that the average kinetic energy is proportional to the temperature.

genius_generous answered 1 year ago

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