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Kinetic Theory

Fuel Rockets Why only liquid-fuel rockets why not solid or gas ? The main issue with solid fuel (or propellant) rockets was that they did not stop burning once launched. This limits the control on the combustion of solid fuel. The breakthrough came with the advent of liquid fuel rockets, which were designed with the adjustment that could change the amount of thrust at different points of time during flight. Currently liquid oxygen and hydrogen are used as the rocket fuel. In case of gases, it is essential to keep them at extremely low temperatures and high pressures with the necessary thrust at the same time, which is not an easy task with out additional pressure controls. Lets learn more about the gases and their changing behaviour in different conditions.

Learning objectives

After completing the topic, the student will be able to:

  • Discuss about the equation of state of matter and its relevance to the earthly life.
  • Define, discuss and explore the terms mole, molecular mass, Avogadro number and their significance in daily life scenarios.
  • Discuss, examine and investigate about the gas laws and probe for any deviation when applied to real gases.
  • Develop an ideal gas equation and discuss the kinetic theory of gases, molecular speeds with its importance to real world analogies.
  • Analyze mean free path of molecules of a gas and apply them to probe the behavior of the gas.
  • Discuss and explore heat capacity and equi-partition energy of a gas.

Molecule space Conceptual computer artwork of molecules in space The theory of panspermia states that the molecules that form the building blocks of life are found throughout the universe. They arrived at earth from extraterrestrial sources early in its history and may still be arriving today!

When we boil water in a tea kettle, the increase in temperature produces steam that whistles out of the spout at high pressure. If we forget to poke holes in a potato before baking it, the high pressure steam produced inside it can cause it to explode messily. These examples show the relationships among the macroscopic properties of a substance, such as pressure 'P', volume 'V', temperature 'T' and mass 'm' of the substance. But we can also describe a substance using the microscopic properties such as, the mass, speed, kinetic energy and momenta of the individual molecules of the substance.

In fact the microscopic and the macroscopic properties are inter-related. For example, the microscopic collision forces that occur when air molecules strike a solid surface cause atmospheric pressure which is a macroscopic property.

So to study the thermal properties of matter, first we shall look at the macroscopic properties of the substance using the ideal gas laws. Then using the knowledge of momentum and kinetic energy, we can relate them to the microscopic properties. It is valuable to determine a relation between the macroscopic properties, volume, pressure, temperature and the mass of the substance. Such a relation is called as 'equation of state' and the variables in the equation are called 'state variables'. State represents the physical condition in which a particular substance exists.

Hot air balloons Hot air balloons Heating the air inside balloon causes it to expand and some of it to flow out. This lowers the mass and makes the balloon rise.
Equation of state

More specifically, an equation of state is an equation describing the state of the substance or matter under a given set of physical conditions. It is a constitutive equation which provides a mathematical relationship between two or more state variables associated with the matter, such as its temperature, pressure, or volume. Equations of state are useful in describing the properties of fluids, mixtures of fluids, solids, and even the interior of stars.

The most prominent use of an equation of state is to correlate densities of gases and liquids to temperatures and pressures. In few cases the relationship among 'P', 'V', 'T' and 'm' is simple enough that we can express it as an equation. When it is too complicated for that, we can use graphs or numerical tables.

A simple (approximate) equation of state for a solid material is given below. It gives the volume 'V' of the material when the pressure is changed from 'P0' to 'P' and temperature is changed from' T0' to 'T'. 'β' is temperature coefficient of volume expansion (fractional volume change (ΔV/V0) per unit temperature change) and 'k' is the compressibility, negative of the fractional volume change (ΔV/V0) per unit pressure change.

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