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Isothermal Process

Thermodynamics is a branch of science which deals with the change in the properties of system during any physical or chemical change. It mainly involves the change in energy from system to surrounding or vice-versa. When a system shows a change in energy then it undergoes the thermodynamic process. The change in energy is accompanied by change in some parameters like internal energy, pressure, volume, temperature.

There are various types of thermodynamic processes which are mostly occurring in practical cases. Each process is specific and unique with its properties and useful for determining the change in energy and the amount of work which is done for changing the energy of the system; for example, isobaric process, isothermal process, adiabatic process, and isochoric process. It is also possible to complete more than one process at a time; for example, when there is a change in volume and pressure then there is no change in temperature and no heat transfer takes place, this is the combination of adiabatic & isothermal thermodynamic process.

Here we are discussing about the isothermal process in which temperature of the system remains constant during the energy change of system. Let’s discuss about the isothermal thermodynamic process in detail.

 

Isothermal Process Definition

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A process in which the temperature remains constant is called an isothermal process. From the starting of the process till the end, the temperature remains constant.
For the process we have the equation as:
P V = Constant
If a system undergoes changes from the state A to B, considering an isothermal process, the temperature remains constant, i.e., in isothermal surface then,

A - - - - - - - - - - - - isothermal process - - - - -- - -> B
( P1, V1, T ) ( P2, V2, T )

Hence $P_{1}V_{1}=P_{2}V_{2}=nRT$

Work Done in an Isothermal Process

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Work done by the gas is given by,

$\Delta W$ = $\int_{V_{1}}^{V_{2}}$ $PdV$

But, $PV = K$ or constant

$P$ =$\frac{K}{V}$

$\Delta W$ = $\int_{V_{1}}^{V_{2}}\frac{K}{VdV}$

= $K \ln$$(\frac{V_{2}}{V_{1}})$

= $nRT \ln$$(\frac{V_{2}}{V_{1}})$

Work done = $nRT \ln$$(\frac{V_{2}}{V_{1}})$
If we consider the change in internal energy of a gas then it is zero.

dU = 0

By the first of thermodynamics,

$\Delta Q$ = $\Delta W+\Delta U$

$\Delta Q$ = $\Delta W$

So, the heat that is supplied in an isothermal process is used to do work against external surroundings. If the specific heat of the process is considered then an isothermal process is infinity. If we consider the bulk modulus of an isothermal process:

Since $PV = K$

On differentiating

$P dV + V dP = 0$

$P dV = - V dP$

$P$ = $\frac{-VdP}{dV}$

Therefore Bulk Modulus $B$ =$\frac{-dP}{dV}$$V$

Compressibility is also stated by:

$\frac{1}{B}$ = $\frac{1}{P}$

The formula for an isothermal process considering it as reversible the Work done is given by:

$W_{(1-2)}$ = $nRT$$\frac{V_{2}}{V_{1}}$

The process from state 1 to state 2

Isothermal Process Examples

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There are various examples of processes where the temperature of the system = K or constant. Some of them are:
  1. Assume a beaker placed in a tub full of water. Now let the beaker contain the base. Slowly add acid to heat. The acid and base react with each other to form salt. Heat is generated from the process. But as the acid is added slowly it gives time to the reaction to transfer the heat from the beaker to the tub. Hence the heat of the beaker remains constant. This is an example of isothermal process.
  2. If we boil the water in the open air then it is an example of isothermal process.
  3. If we consider the isobaric phase change reaction then they are isothermal.
  4. If we stretch a rubber band quickly it is an example of isothermal process.
  5. If we assume any process for which the temperature remains constant then it would be a isothermal process. There are many reactions in chemistry for which the temperature remains constant.
  6. Evaporation is also an example of isothermal process.
  7. Condensation is an example of isothermal process.
  8. All the reactions going on in the refrigerator are isothermal as a constant temperature is maintained in it.
  9. The melting of ice at zero degree is an example of isothermal process.
  10. The reaction in a heat pump is an example of isothermal process.
  11. The boiling of water at hundred degrees is an example of isothermal process.
  12. If we perform a reaction and assist it with a heat sink in order to maintain a constant temperature then we will accomplish an isothermal process.
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