# Isothermal compression of ideal gas: Definition, Formula, Work, PV and TS diagram [with Pdf]

Contents

## What is isothermal compression?

Isothermal compression is the process of reducing the volume of a certain mass of fluid, by keeping its temperature constant throughout the process.

Therefore the internal energy of the fluid also remains constant.

Hence, ∆U = 0

## Isothermal compression PV and TS diagram:-

Here is the PV and TS plot for the isothermal compression process.

## Isothermal compression work:-

For isothermal compression process, formula for the work done is given by,

W=-RT\times ln[\frac{V_{2}}{V_{1}}]

Here -ve sign indicates that work is done on the fluid for the compression.

## Isothermal compression formula / equation:-

Some of the formulae used in the isothermal compression process are as follows,

i] PV relation:

The relation between pressure and volume for isothermal compression is given by

[\frac{P_{1}}{P_{2}}]=[\frac{V_{2}}{V_{1}}]

ii] Change in internal energy:

As the value for ∆T is zero, therefore value for change in internal energy is also zero.

du = 0

iii] Heat transfer:

The heat transfer in isothermal compression is given by,

Q=-RT\times ln[\frac{V_{2}}{V_{1}}]

iv] Change in entropy:

The change in entropy during the isothermal process is given by,

\Delta S =-mR\times ln[\frac{V_{2}}{V_{1}}]

v] Change in enthalpy:

The change in enthalpy for the isothermal compression process is zero.

∆h = 0

## Is Isothermal compression possible?

The isothermal process is a quasi-static process which means that the process occurs slowly to remain the system in thermodynamics equilibrium.

But the compression process is a faster process, therefore during compression, the temperature of the system also increases. Hence it is not possible to maintain a constant temperature during the compression process, therefore in actual conditions, isothermal compression is not possible. 