# Isobaric Process

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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 ΔP = 0.

### How is Pressure kept Constant in an Isobaric Process?

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 = P0 + Mg/A, where P0 = 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 Vi to Vf 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 Vi to Vf on the x-axis.

### Common Examples of Isobaric Process

Boiling of water: As the water boils, the steam formed expands to a volume that is approximately 1600 times of the initial volume and is kept under constant atmospheric pressure.

The conversion of water to ice or freezing is also an example of an Isobaric Process.

Work Done by Gas in an Isobaric Process

Work done by gas in any process is calculated as,

W = ∫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 = PΔV = P x (Vf - Vi).

If the gas expands isobarically, work done = +ve.

If the gas contracts isobarically, work done = -ve.

Thus, the work done is found by calculating the area under the PV curve and its sign depends on whether the gas contracts or expands.

### First Law of Thermodynamics in Isobaric Process

Molar heat capacity is the heat given per mole per unit rise in the temperature of a gas, when this heat is supplied at a constant pressure it is called as Molar Heat Capacity at constant pressure and denoted by Cp = (ΔQ/nΔT)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 ΔQ = ΔU + ΔW.  Applying, we get

(dQ)p = dU + PdV……. (i)

(at constant volume dV = 0, therefore W=0, from the first law of thermodynamics ΔQ = ΔU 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

(dQ/ndT)p = (dQ/ndT)v + (nRdT/ndT)

And as we know (dQ/ndT)p = Cp.

Similarly, (dQ/ndT)v = Cv.

Putting these values, we get,

Cp = Cv + R.

Q1) Which of the following is true for an Isobaric Process :

1. dP = 0

2. dV = 0

3. dT = 0

4. dQ = 0

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

Option A.

Q2) What is the work done in an Isobaric Process?

Answer: In an isobaric process the work done by the gas on the surroundings decreases the internal energy and temperature of the gas. So the total amount of heat added to the gas increases the internal energy and temperature of the gas.

Q3) Give an example of an Isobaric Process.

Answer: The reversible expansion of an ideal gas is an example of an isobaric process. In this process, the heat is converted to work when an expansion is carried out on different working gas or the surrounding gas pressures.

Q4) What is the difference between the Isobaric and Isochoric Process?

Answer: An isochoric process is a chemical process that takes place in the thermodynamic system under a constant volume while in the case of an isobaric process the thermodynamic system is under constant pressure.