Heat and Thgermodynamics

Fluids and Solids
A fluid is a collection of molecules that are randomly arranged and held together by weak cohesive forces and by forces exerted by the walls of the container. A fluid can flow continuously under the application of a force. However, the solid substance does not deform continuously under the application of force. If the solid is deformed then it may come back to its original shape when the applied deforming force is removed ot it may not be able to regain its original shape and size. II).either of the case, the deformation is not continuous rather it takes place in a discrete manner. All liquids and gases are fluids. It is worth noting that the fluids are subset of the phases of matter including liquids, gases, plasmas, .and to some extent plastic solids.
A solid has a definite volume and shape where as a fluid does not.
The fluids have the ability to flow unlike solids.
The fluids form a free surface unlike the solids that form rigid surfaces.
The fluids satisfy the conservation laws including the conservation of mass, linear momentum, angular momentum, and conservation of energy. The solids may or may not satisfYthese conservation laws.
Pressure and Density:
Pressure in general is the force exerted per unit area. When a solid material is merged in a fluid, the force (F) exerted perpendicularly on the surface per unit area of the solid substance is called pressure (P):
P = F/A
where A is the surface area of the solid material placed in the fluid. The unit of pressure is Pascal.
Density in general is defined as mass per unit volume of the substance: p = M/V, where p is the density of the considered object, M is the mass of the substance and V is.its volume. The unit of density is kg/m3.
Density explains how tightly the molecules of a material are packed. However, it has nothing to do with the hardness of a substance.
For an incompressible fluid the density is always constant. Water may be considered as an incompressible fluid at times.
Pascal's Principle:
A change in the pressure applied to a fluid is transmitted undiminished to every point of the fluid and to the walls of the container. In simpler words it can be stated as "the pressure applied to an enclosed fluid is transmitted equally to all points of the fluid and therfore to all walls of the vessel containing the fluid. Hydraulic press is a very good obvious example for this law / principle. It is shown below:
Since the pressure must be same everywhere:
Pat 1 = Pat2
Since pressure = force / area, thus, F1 / A1 = F2 / A2 or F2 = (F1 / A1) x A2. Therefore, the force at the outlet (2) is augmented by the size of the area of the outlet!
Archimedes's Principle
When an object is partly or wholly immersed in a fluid, it is exerted by
an upward force called buoyant force. The magnitude of the buoyant force is equal
to the weight of the fluid displaced by the object. This is called Archimedes's
principle. It can be noted that the buoyant force acting on the object is always in
the vertically upward direction and through the center of gravity of the displaced
fluid. And, this principle is valid as long as the surface tension on the body is
neglected.
The weight of the fluid displaced is directly proportional to the volume of the displaced fluid. Thus, among objects with equal masses, the one with greater volume has greater buoyancy.
If the density of an object is greater than the density of the fluid, then the upward buoyant force is less than the downward force of gravity and the unsupported object sinks.
At neutral buoyapcy the buoyant force is balanced by its weight.
An object's buoyancy reduces with the compression of the fluid and increases with the expansion of the fluid.
Measurement of Pressure:
The fluid pressure can be measured by open-tube monometer or with the help of mercury barometer. One end of the U-shaped tube containing a liquid (figure a) is open to the atmosphere while the other end is connected to a system of unknown pressure P. The difference in pressure P - Po is pgh. Hence P = Po + pgh. The pressure P is called absolute pressure and the difference P - Po is the gauge pressure. Trtehter one is usually measured through gauge scale.
Another type of instrument used to measure the pressure is called barometer (figure b) This instrument follows the rule Po = pgh; h is the height of the mercury column
Surface Tension:
Surface tension is defined as the force experienced (F) by a molecule present on a line (1) of the considered fluid. This happens because of the cohesive force between the liking molecules in a fluid.
The cohesive forces between molecules are shared with the neighboring molecules. Those on the surface have no neighboring molecules above and exhibit stronger attractive, forces. upon the nearest neighbors on the surface. This enhancement of the. intermolecular attractive forces at the surface is called surface tension. Surface teflsion of water at 25°C is 72 dynes/em. The surface tension of water decreases with increase in temperature.
Hot water is a better cleaning agent since it has lower surface tension.
Small insects can walk on the water surface since they have very less. weight.
Soaps and detergents help in lowering the surface tension so that the washing of clothes are possible in better way
General Concepts of Fluid Flow
When a fluid flows its movement can be characterized in one of the two types: steady or laminar and turbulent.
A fluid flow is laminar if each particle of the fluid follows a smooth path such that the paths of different particles never cross each other. And in the steady flow the velocity of the fluid at any point remains constant.
A fluid now is turbulent after certain limit of speed so that the flow becomes Irregular characterized by small whirls.
To characterize the degree of internal friction of the tluid the tenn viscosity is used, Due to the viscosity. a part of the kinetic energy of the fluid is converted to internal energy.
An ideal fluid can be considered to be non-viscous. incompressible with steady and ir-rotational flow
In the ir-rotarional flow the tluid has no angular momentum about any point.
The density' is constant for an incompressible fluid,
the velocity' in a stead} !low is constant at eaeh point of the fluid.
An object moving through a non-viscous fluid c:xperiences zero viscosity.
Application of Bernoulli's Equation
Some of the applications of Bernoulli Equation and Equation of continuity are given as follows:
(1) The lift on an aircraft wing can be explained with the help of Bernoulli Effect.
(2) A golf ball is made to spin when struck by the clud. The spinning ball experiences a lifting force that allows it to travel much farther than it would if it were not spinning. This can be explained by the Bernoulli Equation.
(3) As the water flows from a faucet, the stream of water becomes narrower as it descends since the speed increases. This can be explained by the question of continuity.
Feilds of Flow:
The fields of flow are considered as the speed and direction of flow of the fluids like air. water etc. The molecular motion is important in all these fluids.
Viscosity, Turbulence and Chaotic flows:
Viscosity is the characteristic of the fluid which arises as there is a resistance force coming into play in between two layers of fluid which move in a relative motion with each other. It characterizes the degree of the internal friction in the fluid. It can be noted that the viscosity causes part of the kinetic energy of a fluid to be converted to internal energy. This is similar to the mechanism of the object sliding on a rough horizontal surface, which loses kinetic energy.
When the particles in the fluid move in a smooth path and constant reasonable speed the flow is usually called steady or laminar flow. And if the fluid flows in a speed just above a critical speed, then the flow is turbulent. The turbulent flow is irregular and is charcterized by small whirlpool like regions. These regions are called eddies. These eddies can vary in size with the extent of turbulence present in the fluid.
The flow becomes chaotic if the motion of the fluid becomes very much disorder or irregular even more as that of the turbulent flow.
Gases: Boyle's Law and Charles's Law
For most gases and under a wide range of conditions, the ratio of volume to temperature, for a gas at constant pressure, is constant; V/T = constant. This is known as Charles Law.
For most gases and under a wide range of conditions, the product of pressure and volume, for a constant temperature, is constant; PV = constant. This is known as Boyle's Law.
Charles' and Boyle's Law may be combined as PV/T = constant or PV/T = PoVo / To
For constant volume:
P / T = Constant
P / T = Po / To
For constant temperature:
PV = Constant
PV = PoVo
This is known Boyle's Law.
For constant pressure:
V / T = constant
V / T = Vo / To
This is known as charles' Law.
Combining these, we have
PV / T = constant
PV / T = PoVo / To
PV = [constant] T
PV = n R T
This is known as the ideal gas law.
n = number of moles
A mole of gas molecules is Avagardro's number NA of molecules,
NA = 6.02 x 1023
R = universal gas contant
R = 8.314 J/mole-K
Pressure is caused by the constant bombardment of the many individual molecules of a gas.
The ideal gas law can be explained by the constant bombardment of the many individual molecules of a gas.