A monatomic ideal gas expands at constant pressure. (a) What...

Name: Problem 40, Chapter 15: Physics
Uploaded: 2020-04-11T14:25:00-08:00
Duration: 5 min 2 s
Channel: Yaqub Khan
Description: A monatomic ideal gas expands at constant pressure. (a) What percentage of the heat being supplied to the gas is used to increase the internal energy of the gas? (b) What percentage is used for doing the work of expansion?

A monatomic ideal gas expands at constant pressure. (a) What percentage of the heat being supplied to the gas is used to increase the internal energy of the gas? (b) What percentage is used for doing the work of expansion?

Key Concepts

Monatomic Ideal Gas

A monatomic ideal gas is a theoretical gas where the particles are non-interacting single atoms. Its internal energy is solely a function of its temperature, with each atom contributing only translational kinetic energy. This characteristic simplifies the analysis because the degrees of freedom are fixed, and formulas for internal energy and work done can be directly applied without needing to consider rotational or vibrational modes.

Constant Pressure Process

A constant pressure process is a thermodynamic process in which the pressure remains unchanged as the system evolves. In such a process, the volume and temperature of the gas can change, and the work done by the system is given by the product of pressure and the change in volume. This condition notably affects the distribution of supplied heat between increasing the internal energy and doing work on the surroundings.

First Law of Thermodynamics

The first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system (?U = Q - W), is fundamental in analyzing energy transfer processes. It provides a framework to partition the input heat into the portion that increases the internal energy of the gas and the portion that is expended in doing work during expansion.

Heat Capacities

Heat capacities, such as the constant-volume specific heat (C_V) and the constant-pressure specific heat (C_P), describe how much energy is needed to raise the temperature of a gas under different constraints. For a monatomic ideal gas, these values are well-defined (with C_V = (3/2)R and C_P = (5/2)R), and they are critical for determining the proportions of heat used to increase internal energy versus performing work during a constant pressure process.

Please give Ace some feedback