11.2: Energy Transmission Using a Pneumatic System
- Page ID
- 116668
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Understanding Gases and Their Behavior
Before diving into the concept of energy transmission through a gas, it is essential to first define what a gas is and explore its characteristics. Gas is composed of moving molecules that, unlike those of solids or liquids, do not readily attract one another. Because of their energy and lack of binding forces, gas molecules must be contained; otherwise, they will disperse into the surrounding space.
In a confined space, gas molecules constantly move, crashing into one another and the walls of the container, similar to a swarm of bees. This movement, called molecular energy, enables gas to take the shape and fill the volume of any container. A large portion of the volume of gas is empty space, which allows it to expand and take any shape.
Molecular Energy and Heat
To better understand gas behavior, it's helpful to first examine what heat energy is. In solids, heat energy is the vibration of molecules, which increases with temperature. In liquids, the molecules are in contact but not rigidly positioned; they slide past one another, with heat energy manifesting as molecular movement. Similarly, in gases, molecules are always in motion, and higher temperatures result in faster movement of these molecules. The relationship between temperature and pressure in gases is crucial for understanding pneumatic systems.
When gas is housed in a container, the speed of the molecules determines its temperature, while collisions with the container walls create pressure. These molecular collisions occur millions of times per second; a pressure gauge connected to the container would interpret these collisions as a single pressure value. By manipulating gas properties—such as temperature, pressure, and volume—the behavior of gases can be predicted using principles like the Ideal Gas Law, which states:
PV = mRT
Where:
- "P" is absolute pressure,
- "V" is total volume,
- "m" is the number of moles,
- "R" is the universal gas constant (2271.87 Joules/mole),
- "T" is absolute temperature.
For practical applications, such as industrial pneumatic systems in reference to pressure, volume, and temperature, the ideal gas law can be simplified into 3 primary equations:
Boyle's Law
The first equation is Boyle's Law, which states:
P₁ x V₁ = P₂ x V₂
Where:
- PPP is absolute pressure,
- VVV is volume
Gay-Lusaac's and Charles's Laws
Next is Gay-Lusaac's Law, which states:
P₁ / T₁ = P₂ / T₂
Where:
- "T" is absolute temperature.
And Charles's Law, which states:
P₁ / T₁ = P₂ / T₂
When air is compressed, its pressure and temperature increase, but when it is allowed to expand, both temperature and pressure decrease. This phenomenon is critical for understanding how pneumatic systems operate and how force is generated.