Isothermal Expansion

Introduction

An isothermal process is a type or form of the thermodynamic process where the temperature (T) of the system (s) remains constant (c), that is ΔT=0. This process occurs generally when the system remains in contact with an outside (o) thermal reservoir, and also a change in the system (s) occurs slowly (s) enough to permit the system to be continuously adjusted or fixed to the temperature (T) of the reservoir through the heat (ΔH) exchange.

For an ideal gas, all the collisions between (b/w) molecules or atoms (a) are perfectly (completely) elastic and there is no intermolecular force (F) of attraction found in an ideal gas because the molecules (m) of the ideal gas (g) move very fast and also, they are far apart from each other so that they can’t interact with each other. So, they can easily expand at a constant temperature.

What is Isothermal Expansion?

Isothermal expansion is defined as the expansion of gas (or air) under a certain constant temperature (T). Since the air (a) does work (w) on expanding so it loses heat, consequently, heat (ΔH) must be added or provided to the air to maintain it at provided constant temperature. For an ideal gas (g) molecules have zero or no volume (v) and they do not interact. Now, according to the ideal gas law, pressure (p) varies or changes linearly (l) with the temperature (T) and quantity (q) but is inversely proportional with the volume (v), that is pV=nRT, in this equation (eq) the symbol R is a constant called the universal gas (g) constant that occupies the same value for all gases (g). And, the isothermal process (p) can be expressed with the ideal gas (g) law as pV=constant or,p₁ V₁=p₂ V₂.

P-V Diagram to Represent Isothermal process

Zátonyi Sándor (ifj.), Fizped, Izoterm pV munka, CC BY 4.0

For an isothermal type process, $\mathrm{pV=constant or,p_1 V_1=p_2 V_2\: or,\: P\propto \frac{1}{V}}$. As we know that for an isothermal process, the temperature (T) remains constant. In a PV diagram, the process represented would be an isothermal type if the product (multiple) of the value (v) of the Pressure (P) and the volume (v) remain constant, that is pV=constant, whatever the constant value. The value for the constant will completely depend on the temperature (T), but it remains constant (c) if the temp (T) stays constant.

Equations to define Isothermal Expansion

For an isothermal process, when the internal energy (ΔU) of the system changes, then it is given or depicted by the following condition −

$$ΔU=q+w ....(1)$$

where ΔU represents the change in the internal energy, q denotes the heat given by the respective system and, w denotes the amount of work done over the system.

$$\mathrm{ΔU=q+p_{ex} ΔV}$$

Since, $\mathrm{w (work\: done) = p_{ex} ΔV}$, this is the work done under the vacuum condition. So, equation - (1) can also be written in this form. Now, let’s take an example of an ideal gas (g) like Helium (He) subjected to isothermal expansion (e) in the presence (p) of vacuum (v). So, the work done (W.D) for this vacuum case will be NIL or null, that is w=0 or p_ex=0. So, according to the experiments (e) of Joule, q=0 and hence, it is concluded that the work done (W.D.) is NIL (i.e.) that is ΔU=0.

Examples

Some examples of isothermal processes are as follows −

• Changes made either in the state or in the phase of different liquids (l) with the help of process (p) of melting (m) and evaporation (e) are examples of the isothermal process (p).

• One of the examples (e) of the industrial (i) application of the process or isothermal process (p) is the Carnot engine. In this particular engine, some of the parts are taken out isothermally.

• The Refrigerator also works in this concept. A set of changes that takes place in the working of a refrigerator but the temperature (T) inside it remains constant.

• The Heat pump is another example based on the isothermal process.

Difference Between Isothermal and Adiabatic process

Isothermal Process	Adiabatic process
The transfer of heat takes place.	There is no transfer of heat in this process.
In this process, for any given amount of volume (v), the pressure (p) is more followed by the ideal gas equation.	In this process, at a given amount of volume (v), the pressure (p) is less or low.
In this process, the temperature denoted by T remains constant.	In this process, the temperature (T) changes because of the change in the internal energy (e) of the system.
From the thermal (t) reservoir present near the system (s), either the heat (H) can be added or removed (taken out) from the system (s) to keep the temperature constant.	Here, there is no change in the heat (H) and so, there is no addition (add) or subtraction (subs) of the heat.
Slow processing of the transformations.	Fast processing of the transformations.

Conclusion

In thermodynamics (a branch of chemistry), the process or an isothermal process (p) is a type or form of the thermodynamic process where the temperature (T) of the system (s) remains constant (c), that is ΔT=0. This process occurs generally when the system remains in contact with an outside (o) thermal reservoir, and also a change in the system (s) occurs slowly (s) enough to permit the system to be continuously adjusted or fixed to the temperature (T) of the reservoir through the heat (ΔH) exchange. For an ideal gas, all the collisions between (b/w) molecules or atoms (a) are perfectly (completely) elastic and there is no intermolecular force (F) of attraction found in an ideal gas because the molecules (m) of the ideal gas (g) move very fast and also, they are far apart from each other so that they can’t interact with each other. So, they can easily expand at a constant temperature.

FAQs

1.What do you mean by thermal reservoir?

A thermal reservoir is a thermodynamic system type with a heat capacity (ΔC) so large that the temperature (T) of the reservoir changes a little bit when a more affordable amount of heat is either added or extracted.

2.What is the meaning of perfectly elastic collision?

In a perfectly elastic collision, there is no net (overall) conversion of the kinetic energy (K.E.) into other forms.

3.Write the ideal gas law equation.

The ideal gas law equation is − pV=nRT where p= pressure, v= volume, n= moles, R= gas constant, and T= temperature.

4.Mention two uses of the isothermal process.

• It is used in the Carnot cycle.

• It is also used in the heat pump.

5.What is the adiabatic process?

It is described as a process in which no heat transfer takes place between the system (s) and the surrounding.