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# Isobaric Process

Last updated date: 22nd Jul 2024
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## Isobaric Process – Common Examples and First Law of Thermodynamics.

Thermodynamics refers to that branch of physics which deals with understanding how thermal energy is related to all other forms of matter. This indicates that heat energy has the ability to affect all other forms of energy, such as kinetic energy, potential energy, and so on. The study that deals with understanding how heat energy can be converted to other forms of energy is known as thermodynamics.

Heat, as a form of energy, can be conserved or transferred to another medium but can never be destroyed. This indicates that thermal energy can be converted to other forms of energy. The practical implications of this function is the reason why we have electricity and heavy machinery. All these processes convert thermal energy to other forms of energy.

What is a Thermodynamic Process?

A thermodynamic process is said to have occurred if a system changes its state, where the state refers to its physical properties. The system returns to its original state when all these properties return to their initial or original state. If a thermodynamic process is occurring at a constant external pressure then the process is said to be an Isobaric Process or a thermodynamic process where the pressure of the system remains constant or $\triangle P = 0$.

The term ‘isobaric’ is derived from two Greek words- ‘iso’ and ‘baros’. These words mean equal and pressure, respectively. Therefore, the term indicates that pressure remains the same while heat is transferred to the system along with changes in internal energy.

How is Pressure kept Constant in an Isobaric Process?

It can be noted here that isobaric processes are also referred to as constant pressure processes.

To understand this assume a cylinder containing gas with a movable piston on one end and a mass M kept on the piston.The pressure applied to the piston is $P = P_{0} + \frac{Mg}{A}$, where $P_{0}$ = The pressure of the atmosphere and A = Area of the piston.

Now the cylinder is slowly heated from the bottom, the process is carried out slowly so the gas and the piston are always in equilibrium and the process is a ‘quasi-static’ process.

The small amount of heat (dQ) supplied to the gas is used partially in increasing its volume by a small amount (dV) and partially in increasing its internal energy by (dU).

The piston slowly rises up as the gas expands. It is pushed by the gas as excess pressure is developed inside due to the supply of heat the pressure applied by the piston doesn’t change as the mass M is constant and atmospheric pressure is also constant so the piston rises and the excess pressure is adjusted by the increase in volume thus keeping the pressure constant and maintaining the equilibrium between the piston and the gas. This process is carried out until the gas has reached the required temperature or required volume, keeping the pressure constant. The volume rises from $V_{i}$ to $V_{f}$ and the pressure doesn’t change until the mass M changes.

This process is known as the Isobaric Expansion of gas, if the volume decreases then the process is known as the Isobaric Contraction of gas and these comprise the Isobaric Process. In isobaric contraction, the gas loses heat.

On the P-V graph, this process is shown as a horizontal line extending from $V_{i}$ to $V_{f}$ on the x-axis.

### What are the Types of Isobaric Processes?

Isobaric expansion- this refers to when there is an increase in the volume accompanied by a fall in temperature.

Isobaric contraction- this refers to when there is a decrease in volume accompanied by a rise in temperature.

Pressure remains constant in both these cases.

### What are Some Examples of an Isobaric Process?

We can find examples of all physical processes in our day-to-day life. While the principle remains the same, the only difference is that in big industrial plants, they happen in a much larger and controlled environment.

One of the best examples of an isobaric process can be the process through which water boils and gets converted into steam. In this process, when steam is formed, it has a considerably higher volume. However, since the external atmospheric pressure remains unchanged, it is an example of an isobaric process.

Similarly, the freezing of water into ice is another example of an isobaric process.

### Work Done by Gas in an Isobaric Process.

Work done by gas in any process is calculated as, $W = \int d(PV)$,

as pressure is constant in the Isobaric Process, the equation changes to,

$W = P \int_{v_{i}}^{v_{f}} dV$, if we look at the PV curve this comes out to be the area under the PV curve.

Or, $W = P \triangle V = P \times (V_{f} - V_{i})$.

In case the expansion of gas is isobaric, then the work done is positive. When the contraction of gas is isobaric, then the work done is negative.

The net work done can be found by calculating the rectangular area under the PV curve as mentioned. The sign would depend on whether there was expansion or contraction of the gas.

### How Does The First Law of Thermodynamics Apply in an Isobaric Process?

The first law of thermodynamics states that any change in the internal energy of a given system (U) will be the same as the difference between the amount of thermal energy added to that system (Q) and the net work that is done by that system (W).

Molar heat capacity is the heat given per mole per unit rise in the temperature of a gas.  If this thermal energy is supplied when pressure remains constant, it is called Molar Heat Capacity at constant pressure.

This is denoted by $C_{p} = (\frac{\triangle Q}{n\triangle T)}p$, where the subscript ‘p’ denotes constant pressure.

As discussed earlier, the heat supplied to the gas in an isobaric process goes partially in increasing its volume by a small amount (dV) and partially in increasing its internal energy by (dU).

From the First Law of Thermodynamics, $\triangle Q = \triangle U + \triangle W$.  Applying, we get

(dQ)p = dU + PdV……. (i)

(at constant volume dV = 0, therefore W=0, from the first law of thermodynamics $\triangle Q = \triangle U$ or heat supplied at constant volume = change in its internal energy). So, dU = (dQ)v.

Therefore equation becomes,

(dQ)p = (dQ)v + PdV……. (ii)

For an Ideal Gas, PV = nRT,

Therefore,

PdV = nRdT,

So,

(dQ)p = (dQ)v + nRdT……. (iii)

From here we also can prove

Cp = Cv + R

Dividing (iii) by ndT we get

$(\frac{dQ}{ndT})p = \frac{dQ}{ndT}v + \frac{nRdT}{ndT}$

And as we know,

$(\frac{dQ}{ndT})p = Cp$.

Similarly, $(\frac{dQ}{ndT})v = Cv$.

Putting these values, we get,

Cp = Cv + R.

## FAQs on Isobaric Process

1. Which of the following is true for an Isobaric Process :

1. dP = 0

2. dV = 0

3. dT = 0

4. dQ = 0

An isobaric process is a thermodynamic process where the pressure remains constant i.e. dP = 0.

Option A.

2. What is the main difference between isobaric and isothermal processes?

In an isobaric process, the pressure of the system remains constant, while in an isothermal process, the temperature of the system remains constant. When temperature remains the same, the pressure becomes inversely related to the volume. Isothermal expansion refers to a decrease in pressure, whereas isothermal compression indicates an increase in pressure. There are several kinds of thermodynamic processes, and in each of them, one of the factors is held constant. It is important to understand the relationship between the factors as well, since there may be different results to an increase or a decrease in any of the factors.

3. What are some other examples of isobaric processes?

A very commonly observed example of an isobaric process at work is seen in hot air balloons. The hot air inside the balloon makes it lighter in proportion to the cooler air outside it, which makes the balloon rise up. The pressure both in and out of the balloon remains the same, however, the temperature of the gasses becomes different. When heat is injected into the air inside the balloon, it rises up. A part of the heat is converted into work, which makes the balloon rise up in the air.

4. What happens to the internal energy of a system when it undergoes isobaric expansion?

During an isobaric expansion, heat is injected into the system. The pressure of the system remains constant and unchanged on principle. The injected heat is then used up in two ways. A part of this heat goes to increase the internal energy of the system. The rest is used up by the said system for work. However, this works on the assumption of an ideal gas. The internal energy of the system will increase since heat also goes into the system.

5. What is the difference between isobaric process and isochoric process?

In any isobaric process, the pressure of the system is always constant. Heat is transferred into the system, which does work and increases the internal energy of the system. In case of an isochoric process, the volume of the system always remains constant. This is also sometimes known as an isometric process. In this, the temperature is directly proportional to the pressure. Due to unchanging volume, it is not possible to do any work on the system. The total amount of heat that is supplied to or rejected from the system is the same as the increase or the decrease of internal energy of the system.

6. In an isobaric process, how can the net work done be calculated?

An isobaric process works on the assumption that the pressure in the system is always at a constant. Due to this, the force exerted on the system is also constant and the resultant work done is denoted by $P\triangle V$. The pressure inside the system is the same as the atmospheric pressure. This means that the system is connected to a constant-pressure reservoir through the use of a movable boundary. In order for the gas to expand or contract while the pressure in the system remains constant, the supply of heat needs to be managed effectively.