What is an isothermal process?

It’s a constant temperature process

It's?the?process?wherein?the?system's?temperature?either?stays?constant?or?is?compelled?to?stay?constant?despite?changes?in?other?physical?quantities.

What components make up the isothermal process?

Generally speaking, isothermal processes are very slow in nature. Since an ideal gas's internal energy is temperature-dependent, the change in internal energy for an ideal gas during an isothermal process is zero, or ΔU = ΔT = 0

Therefore, the equation U = Q - W converts to Q = W

U = Internal energy, Q = Heat energy, W = Work

An ideal gas is a hypothetical gas in which there are no intermolecular attractions between molecules and the collisions of the molecules with container walls are elastic.

An ideal gas follows ideal gas laws, PV = n RT. The pressure is inversely proportional to volume. PV = K [Constant]

The value of K = n RT

This means PV = n RT

P = n RT / V = Constant / V [ at constant T]

Here,

n is the of moles of gas

R = Ideal gas constant = 8.31 J / K – mole

V is m3 of gas

P is expressed as Pascal

Requirements for an isothermal process

-The process should be carried out slowly so that there is enough time for compensation of heat if it is lost during heat transfer from the surroundings.

-The boundaries of the system must be enough conducting so that heat can flow into the system and exit from the system with no losses.

-The boundaries of the system should be thin so that the resistance on the path of heat transfer by conduction is minimal.

In an isothermal process, with Q = W, means that any heat Q entering converts to work completely as it exits the system.

Work done in isothermal process W = n RT ln V final / V initial

What does this equation mean?

The work done in an isothermal gas expansion can be calculated using the equation W = nRT ln (Vf /Vinitial),

?where:

- W represents the work done

- n is the number of moles of gas

- R is the gas constant

- T is the temperature of the gas in Kelvin

- ln is the natural logarithm

- Vf is the final volume of the gas

- Vi is the initial volume of the gas

This equation captures the work done when a gas undergoes an isothermal (constant temperature) expansion. In an isothermal process, the temperature of the gas remains constant, and so does the product of the pressure and volume, which is equal to nRT. The equation W = nRT ln (Vf /Vi) is derived from the relationship between work done and the change in the state variables of the gas.

During an isothermal expansion, the gas works against the external pressure as it expands, and the equation quantifies the work done in terms of the initial and final volumes of the gas. The natural logarithm in the equation captures the proportional relationship between the work done and the change in volume of the gas, and the gas constant R accounts for the properties of the gas.

In summary, the equation W = nRT ln (Vf /Vi) provides a quantitative measure of the work done during an isothermal gas expansion, taking into account the initial and final volumes of the gas, the number of moles, and the gas constant. It is a fundamental equation in thermodynamics and is used to analyze and understand the behavior of gases undergoing isothermal processes.