Isobaric Process: Relations & Work Done | chemca

chemca.in

Home Articles Quizzes About

Thermodynamics

Isobaric Process: Work Done & Relations

Understanding thermodynamic changes at constant pressure.

By chemca Team • Updated Jan 2026

An Isobaric Process is a thermodynamic process in which the pressure of the system remains constant throughout ($\Delta P = 0$). This is common in open systems or reactions occurring in open vessels under atmospheric pressure.

1. State Variables Relation (Charles's Law)

From the ideal gas equation ($PV = nRT$), if Pressure ($P$) is constant: $$ V \propto T $$

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

Volume is directly proportional to Absolute Temperature.

Graph: The PV diagram is a horizontal straight line parallel to the Volume axis.

2. Work Done in Isobaric Process

Since pressure ($P$) is constant, it can be taken out of the work integral $\int P dV$.

Work Done Formula

$$ w = -P_{ext} (V_2 - V_1) = -P \Delta V $$

Using Ideal Gas Law ($P\Delta V = nR\Delta T$):

$$ w = -nR(T_2 - T_1) = -nR\Delta T $$

3. Heat and Enthalpy

Heat exchanged at constant pressure ($q_p$) defines the Enthalpy Change ($\Delta H$).

$$ q_p = \Delta H = n C_p \Delta T $$

Where $C_p$ is the molar heat capacity at constant pressure.

4. First Law Application

The First Law states $\Delta U = q + w$.
For an ideal gas, Internal Energy ($\Delta U$) always depends on $\Delta T$ via $C_v$.

• Internal Energy: $\Delta U = n C_v \Delta T$
• Heat: $q = n C_p \Delta T$
• Work: $w = -nR \Delta T$

Substituting these back verifies Mayer's Relation:

$$ nC_v\Delta T = nC_p\Delta T - nR\Delta T \implies C_p - C_v = R $$

Knowledge Check

Test your understanding of Isobaric Processes

© 2026 chemca.in. All rights reserved.

Optimized for learning Thermodynamics.

Quiz Revision Notes Downloads Class Notes Video Lectures