Name: Macroscopic and Microscopic Variables
Uploaded: 2019-07-19
Duration: 5 min 3 s
Description: This video enables students to understand the definition and examples of the macroscopic and microscopic variables of the thermodynamic system.

Question

Explain the isobaric process and derive the work done in this process.

Accepted Answer

A thermodynamic process that occurs at constant pressure. Even though pressure is constant in this process, temperature, volume and internal energy are not constant.
From the ideal gas equation,

$V = (\frac{μR}{P}) T$

$Here, \frac{μR}{P} = constant . . . . . . . . . . (1)$

Temperature is directly proportional to volume in an isobaric process.
$V \propto T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)$

In isobaric process, the $V - T$ graph is a straight line passing through the origin.

If a gas goes from a state $(Vi, Ti) to (Vf, Tf)$ at constant pressure, then the system satisfies the following equation $\frac{T_{f}}{V_{f}} = \frac{T_{i}}{V_{i}} . . . . . . . . . . . . . . . . (3)$

Most of the cooking processes in our kitchen are isobaric processes. The PV diagram for an isobaric process is a horizontal line parallel to volume axis. Figure (a) represents isobaric process where volume decreases, figure(b) represents isobaric process where volume increases.

So, the work done in an isobaric process is,
Work done by the gas $W = \int_{V_{1}}^{V_{2}} P d V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (4)$

In an isobaric process, the pressure is constant, so P comes out of the integral, $W = P \int_{V_{i}}^{V_{f}} d V . . . . . . . . . . . . . . . . . . . . . . . . . . . (5) W = P = [V_{f} - V_{I}] = P ∆ V . . . . . . . . . . . . . . . . . . . (6)$

The equation (6) can also be rewritten using the ideal gas equation. From ideal gas equation $PV = μRT and V = \frac{μRT}{P}$

Substituting this in equation (6) we get $W = {μRT}_{f} (1 - \frac{T_{i}}{T_{v}}) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (7)$

The first law of thermodynamics for isobaric process is given by $∆ U = Q - P ∆ V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (8)$
Above equation depicts work done in isobaric process.

Explain the isobaric process and derive the work done in this process.

Important Questions on Heat and Thermodynamics

Learn and Prepare for any exam you want !