Thermodynamic processes on an ideal gas

In this note we discuss isothermal, adiabatic, isobaric, and isochoric processes with an ideal gas. We begin by recalling a few basic principles from thermodynamics, and their application to a container of ideal gas, as shown in the figure below.

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A container of ideal gas.

When the gas is at an absolute temperature T > 0, the molecules of the gas move around inside the container and bounce off its walls. Each gas molecule suffers a change in momentum upon such a collision, and the totality of all those collisions per unit time exerts a force on the walls of the container. …

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Optics without ray diagrams: Mirrors

The usual discussions of geometrical optics often rely too heavily on ray diagrams to locate the image and study its properties. We will demonstrate that all of these insights can be obtained purely by algebra on the mirror equation. Developing these instincts will help us solve optics problems without having to use crude, hand drawn, and often inaccurate ray diagrams. Our main results are summarized in the table below.

We begin by recalling the mirror equation

(1)   \begin{equation*}   \frac{1}{p} + \frac{1}{q} = \frac{1}{f} , \end{equation*}

where p and q the distances of the object and image from the mirror, and the focal length f=R/2, for a spherical mirror with …

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How does Doppler effect work?

The Doppler effect for sound is a perceived difference between the frequency of sound heard by an observer and the actual frequency emitted by a source, due to relative motion between the source and the observer. A familiar example of this phenomenon is the change in sound frequency of an ambulance or fire engine as it rushes past you. We give a visual explanation of this effect and derive the relation between the observed and emitted frequencies below.

First, recall that the velocity of sound in a medium, v, is a property of the medium alone. That is, after the …

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