What Is an Isobaric Process?

An isobaric process is a fundamental thermodynamic process in which the pressure of a system remains constant while other state variables, such as volume and temperature, may change. This type of process is common in many physical and engineering systems and is essential for a clear understanding of heat and work interactions during constant pressure transformations.

Isobaric Process: Definition and Basic Characteristics

An isobaric process occurs when the pressure of a thermodynamic system remains unchanged throughout the process, denoted mathematically as $\Delta P = 0$. During an isobaric transformation, both the volume and temperature of the system can vary, but the applied pressure is constant.

The term 'isobaric' is derived from the Greek words 'iso,' meaning equal, and 'baros,' meaning pressure. The volume change at constant pressure leads to heat being transferred into or out of the system, causing the internal energy to change accordingly.

Work Done in an Isobaric Process

When a gas expands or contracts at constant pressure, work is done by or on the system. The work done ($W$) is given by the equation $W = P\,\Delta V = P(V_f - V_i)$, where $P$ is the constant pressure, and $V_i$, $V_f$ are initial and final volumes, respectively.

If the gas expands ($V_f > V_i$), work done by the gas is positive. If the gas is compressed ($V_f < V_i$), the work done by the gas is negative. This relationship is graphically represented as the area under the straight horizontal line on a $P$-$V$ diagram.

For deeper information on energy transformations in physics, refer to Work, Energy, and Power.

First Law of Thermodynamics and Isobaric Processes

The first law of thermodynamics relates the heat supplied to a system ($\Delta Q$), its change in internal energy ($\Delta U$), and the work done ($\Delta W$):

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

For an isobaric process, this equation becomes:

$\Delta Q = \Delta U + P(V_f - V_i)$

In the case of an ideal gas, the change in internal energy depends only on the temperature change and can be written as $\Delta U = nC_V \Delta T$, where $n$ is the number of moles and $C_V$ is the molar specific heat at constant volume.

Further study on the first law can be explored at First Law of Thermodynamics.

Equation of State and Isobaric Condition

For an ideal gas, the equation of state is $PV = nRT$, where $R$ is the universal gas constant. In an isobaric process ($P$ constant), the relationship between temperature and volume simplifies to:

$\dfrac{V_1}{T_1} = \dfrac{V_2}{T_2}$

This indicates that, at constant pressure, the volume of an ideal gas is directly proportional to its temperature.

Specific Heat at Constant Pressure: $C_P$

The specific heat capacity at constant pressure ($C_P$) is the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius at constant pressure. For an ideal gas, the heat supplied in an isobaric process is:

$\Delta Q = nC_P\Delta T$

For ideal gases, the relation between heat capacities is $C_P = C_V + R$.

Analysis of Isobaric Process on $P$-$V$ Diagram

On a $P$-$V$ diagram, an isobaric process is represented by a horizontal line, as pressure remains constant while volume changes. The area under this line corresponds to the work done during the process.

For further exploration of thermodynamic concepts, visit Thermodynamics Overview.

Equation Summary for Isobaric Process

Examples of Isobaric Processes

The boiling of water at atmospheric pressure and the melting of ice are practical examples of isobaric processes. In these situations, heat is absorbed or released, causing phase changes at constant pressure while volume and temperature adjust.

In engineering, the operation of a heat engine or the inflation of a hot air balloon often involves isobaric stages, where pressure remains constant as heat input changes the system's state. Related thermal machines are further discussed in Understanding Heat Pumps.

Solved Example: Calculating Work and Heat in an Isobaric Process

A sample of $2$ moles of an ideal gas is heated at constant pressure to raise its temperature from $300\,\text{K}$ to $400\,\text{K}$. Calculate (a) work done by the gas, (b) heat supplied if $C_P = 29\,\text{J\,mol}^{-1}\text{K}^{-1}$.

Solution:

• Work done: $W = nR\Delta T = 2 \times 8.314 \times (400 - 300) = 1662.8\,\text{J}$
• Heat supplied: $\Delta Q = nC_P\Delta T = 2 \times 29 \times 100 = 5800\,\text{J}$

Key Features of Isobaric Processes

• Pressure remains constant throughout the process
• Volume and temperature change simultaneously
• Work done equals the area under the $P$-$V$ curve
• Heat supplied calculated using $C_P$
• Applicable to both physical and chemical changes

Comparison with Other Thermodynamic Processes

An isobaric process differs from other thermodynamic processes, such as isochoric and isothermal processes. In an isochoric process, volume remains constant, while in an isothermal process, temperature remains constant. For a detailed comparison, see Isothermal vs Adiabatic Processes.

Internal Energy in Isobaric Processes

During isobaric expansion or compression, the internal energy change of an ideal gas depends exclusively on its change in temperature. The supplied heat is partly used to increase internal energy and partly to perform work at constant pressure.

More details on internal energy and thermodynamic transformations can be found in Isobaric Process Explained.