Show that the specific heat ratio of a monatomic ideal gas is equal to 5 / 3

Name: Problem 61, Chapter 3: Fundamentals of Engineering Thermodynamics SI VERSION
Uploaded: 2022-01-13T09:09:00-08:00
Duration: 1 min 37 s
Channel: Manik Pulyani
Description: Show that the specific heat ratio of a monatomic ideal gas is equal to 5 / 3

step 1 To solve this question we have again the same equation 0 equals to H1 minus H2 plus v1 square mi

Show that the specific heat ratio of a monatomic ideal gas...

Key Concepts

Specific Heat Ratio

The specific heat ratio, often denoted by ? (gamma), is the ratio of a gas’s heat capacity at constant pressure (Cp) to its heat capacity at constant volume (Cv). This ratio is essential in understanding adiabatic processes in thermodynamics and depends directly on the molecular structure and degrees of freedom of the gas.

Monatomic Ideal Gas

A monatomic ideal gas is a gas composed of single-atom molecules, meaning the internal energy of the gas is purely kinetic with no contributions from rotational or vibrational motion. This characteristic simplifies the calculations of heat capacities since only translational degrees of freedom are relevant.

Degrees of Freedom

Degrees of freedom refer to the independent modes in which a molecule can store energy. In the case of a monatomic gas, there are three translational degrees of freedom corresponding to motion in three-dimensional space. These degrees determine how energy is partitioned within the gas, influencing its thermodynamic properties.

Equipartition Theorem

The equipartition theorem states that energy is equally distributed among all available degrees of freedom in a system, with each degree of freedom contributing (1/2)kT (where k is the Boltzmann constant and T is the temperature) to the internal energy. In monatomic gases, this principle is used to derive expressions for Cv and Cp, ultimately leading to the specific heat ratio.

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