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# Ideal Gas Equation And Helmholtz Free Energy

An ideal gas is a type of gas that does not exist in a practical scenario but it is an assumption made for the study. Hence it is also known as theoretical gas. Ideal gas condition is an ideal state to study the behavior of the gases. An ideal gas is formed of randomly moving particles. In an ideal gas, the collision of particles is assumed to be perfectly elastic in nature which means no energy of either of these particles is wasted. Hence, the internal energy of the system is in the form of kinetic energy and any change in internal energy is followed by a change in the temperature.

In reality, when gas particles collide with each other, some of their energy is wasted in changing directions and overcoming the friction. However, at Standard Temperature and Pressure conditions, most natural gases behave like an ideal gas when subjected to reasonable restrictions. In certain conditions, many gases like oxygen, noble gases, hydrogen, nitrogen, and some heavier gases like carbon dioxide can be considered as ideal gases under a reasonable tolerance.

Ideal Gas Equationis the mathematical representation of defining the states of the hypothetical gases by the combinations of empirical and physical constants.

From the gas laws, the ideal gas equation can be described by

Pressure (P)

Volume (V)

Temperature (T) = t + 273.15 degree C

As we know, for an ideal gas

PV = K

Hence, theideal gas equation is given by

PV = nRT

where,

P= pressure of the gas;

n= Number of Moles;

V=volume of the gas;

T=Absolute temperature;

R=Ideal Gas constant (Boltzmann Constant)

Now let us learn about another important concept of physics, the Helmholtz free energy.

# Helmholtz Free Energy

Helmholtz free energy is a thermodynamic potential that estimates the amount of useful work that can be obtained from a closed system at a constant volume and temperature.

If negative change is seen in the Helmholtz energy during a thermodynamic process, it is equal to the maximum work done by the system in which volume is held constant.

In conditions when the volume is not held constant, part of this work would be performed as boundary work. This makes Helmholtz energy useful for systems held at constant volume and at constant temperature condition, the Helmholtz energy is minimized at equilibrium.

Helmholtz free energy equation is given as:

F = U-TS

Where,

F: Helmholtz free energy

T: absolute temperature of the surroundings in kelvin
U: internal energy of the system
S: the entropy of the system in joules per kelvin

In contrast to Helmholtz free energy, there exists a concept known as the Gibbs free energy or free enthalpy used as a measure of the thermodynamic potential of the system arises.

Thermodynamic potentials are the quantities that are used to describe the chemical thermodynamics of any reaction and non-cyclic processes. They are the enthalpy, the Helmholtz free energy, internal energy, and the Gibbs free energy. The Gibbs free energy G is defined by

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