Write a system of linear inequalities that represent each problem situation

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Write a system of linear inequalities that represent each problem situation

Thermodynamic temperature The symbol used to represent temperature in equations is T with SI units of kelvins.

write a system of linear inequalities that represent each problem situation

The speed of a gas particle is proportional to its absolute temperature. The volume of the balloon in the video shrinks when the trapped gas particles slow down with the addition of extremely cold nitrogen.

The temperature of any physical system is related to the motions of the particles molecules and atoms which make up the [gas] system. The methods of storing this energy are dictated by the degrees of freedom of the particle itself energy modes.

Kinetic energy added endothermic process to gas particles by way of collisions produces linear, rotational, and vibrational motion. In contrast, a molecule in a solid can only increase its vibrational modes with the addition of heat as the lattice crystal structure prevents both linear and rotational motions.

These heated gas molecules have a greater speed range which constantly varies due to constant collisions with other particles. The speed range can be described by the Maxwell—Boltzmann distribution. Use of this distribution implies ideal gases near thermodynamic equilibrium for the system of particles being considered.

Specific volume The symbol used to represent specific volume in equations is "v" with SI units of cubic meters per kilogram. Gas volume The symbol used to represent volume in equations is "V" with SI units of cubic meters.

When performing a thermodynamic analysis, it is typical to speak of intensive and extensive properties. Properties which depend on the amount of gas either by mass or volume are called extensive properties, while properties that do not depend on the amount of gas are called intensive properties.

Specific volume is an example of an intensive property because it is the ratio of volume occupied by a unit of mass of a gas that is identical throughout a system at equilibrium.

This concept is easier to visualize for solids such as iron which are incompressible compared to gases. Since a gas fills any container in which it is placed, volume is an extensive property. This term is the reciprocal of specific volume. Since gas molecules can move freely within a container, their mass is normally characterized by density.

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Density is the amount of mass per unit volume of a substance, or the inverse of specific volume. For gases, the density can vary over a wide range because the particles are free to move closer together when constrained by pressure or volume.

This variation of density is referred to as compressibility. Like pressure and temperature, density is a state variable of a gas and the change in density during any process is governed by the laws of thermodynamics.

write a system of linear inequalities that represent each problem situation

For a static gasthe density is the same throughout the entire container. Density is therefore a scalar quantity. It can be shown by kinetic theory that the density is inversely proportional to the size of the container in which a fixed mass of gas is confined.

In this case of a fixed mass, the density decreases as the volume increases. Microscopic[ edit ] If one could observe a gas under a powerful microscope, one would see a collection of particles molecules, atoms, ions, electrons, etc.

These neutral gas particles only change direction when they collide with another particle or with the sides of the container. In an ideal gas, these collisions are perfectly elastic.

This particle or microscopic view of a gas is described by the Kinetic-molecular theory. The assumptions behind this theory can be found in the postulates section of Kinetic Theory. Kinetic theory of gases Kinetic theory provides insight into the macroscopic properties of gases by considering their molecular composition and motion.

Starting with the definitions of momentum and kinetic energy[15] one can use the conservation of momentum and geometric relationships of a cube to relate macroscopic system properties of temperature and pressure to the microscopic property of kinetic energy per molecule.

The theory provides averaged values for these two properties. The theory also explains how the gas system responds to change. For example, as a gas is heated from absolute zero, when it is in theory perfectly still, its internal energy temperature is increased.

As a gas is heated, the particles speed up and its temperature rises. This results in greater numbers of collisions with the container per unit time due to the higher particle speeds associated with elevated temperatures.Ask Math Questions you want answered Share your favorite Solution to a math problem Share a Story about your experiences with Math which could inspire or help others.

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Again, note that the last example is a “ Compound Inequality ” since it involves more than one inequality. The solution set is the ordered pairs that satisfy both inequalities; it is indicated by the darker shading. Bounded and Unbounded Regions. With our Linear Programming examples, we’ll have a set of compound inequalities, and they will be bounded inequalities, meaning the.

Defining a Linear Equation. This lesson is on what a linear equation is. And the answer to that question is essentially a linear equation is any pattern of numbers that is increasing or decreasing.

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Mathematics Glossary» Glossary Print this page. Addition and subtraction within 5, 10, 20, , or Addition or subtraction of two whole numbers with whole number answers, and with sum or minuend in the range , , , or , respectively.

Writing a System of Equations