PRESSURE-VOLUME WORK

PRESSURE-VOLUME WORK

Consider a cylinder fitted with a frictionless and weightless non-conducting piston of area of cross section "A" . An ideal gas is enclosed in the cylinder. Let the volume of gas at initial state is "V1". An external pressure "P"is exerted on the piston.

If we supply "q" amount of heat to the system then it will increase its internal energy by DE. "After a certain limit gas exerts pressure on the piston . If piston is free to move, it will be displaced by "h" & volume of system increases from V1 to V2.

We know that pressure is the force per unit area i.e.
P = F/A OR F = PA ........ (i)
We also know that the work done by the gas on the piston is given by:
DW = F d
Where d = displacement of piston = h
Putting the value of F and d ,we get
DW = (PA) h
OR DW = P (Ah)
But Ah = change or increase in volume = DV
Hence
DW = P DV

THERMODYNAMICS

THERMODYNAMICS

Thermodynamics is the branch of science which deals with the interconversion of heat energy and mechanical energy. All those problems that are related to the interconversion of heat energy and work done are studied in thermodynamics. In thermodynamics we discuss different cycles such as Carnot cycle, Rankine cycle, Otto cycle, diesel cycle, refrigerator, IC engines, EC engines, Compressors, turbines and air conditioners.
FIRST LAW OF THERMODYNAMICS

STATEMENT: "During any process total energy of a system and its surroundings is constant."OR"It is impossible to construct a machine which performs work continuously with taking energy from an external source." OR "Energy can neither be created nor destroyed but it can be converted from one form of energy to another form of energy."

MATHEMATICAL REPRESENTATION


Let a system absorbs DQ amount of heat energy. Addition of heat energy increases the internal energy of system from U1 to U2 and some useful work is also performed by the system.Increase in internal energy is given by:DU = U1 – U2andwork done is DWAccording to the first law of thermodynamics: DQ = DU+ DW SIGN CONVENTION:DQ = positive if heat is added to a systemDQ = negative if heat is released from a systemDW = positive if work is done by the systemDW = negative if work is done on the system

APPLICATIONS OF THE FIRST LAW OF THERMODYNAMICS

Heat can be supplied to a thermodynamic system under the following conditions: ISOBARIC PROCESS ISOCHORIC PROCESS ISOTHERMAL PROCESS ADIABATIC PROCESS
ISOBARIC PROCESS
A thermodynamic process in which pressure of the system remains constant during the supply of heat is called an ISOBARIC PROCESS.
EXPLANATION
Consider a cylinder fitted with a frictionless piston. The piston is free to move in the cylinder. An ideal gas is enclosed in the cylinder.
Let the initial volume of the
system is V1 and initial internal energy is U1. Let DQP the gas is heated from
T1 K to T2 K. Addition of heat causes the following changes in the system:
Internal energy increases from U1 to U2. Volume of the system increases from V1 to V2. Temperature increases from T1 K to T2 K. Work (DW) is done by the gas on the piston.
According to the first law of
thermodynamics:
DQ = DU+ DW But DW = PDVThus DQP = DU+ PDV As DV = (V2 - V1) DQP = DU+ P (V2 - V1)
GRAPHICAL REPRESENTATION

Graph between P & V for an isobaric process is a straight line which is parallel to V-axis.

MOLAR SPECIFIC HEAT

"Amount of heat energy required to raise the temperature of one mole ofa substance by one kelvin is called ‘Molar specific heat’".
It is denoted by "Cn"
Mathematically,
D Q = n Cn DTWhere n = number of moles of substanceOR Cn = DQ /n DT
Unit Of Molar Specific Heat
J/mole K OR J mole-1 K-1.
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MOLAR SPECIFIC HEAT OF GASES
Gases have two types of Molar specific heat because it depends whether the gas is allowed to expand or not when heated .
When the volume of the gas is kept constant, its specific heat is called "molar specific heat at constant volume".
When the pressure of the gas is kept constant, its specific heat is called "molar specific heat at constant pressure
MOLAR SPECIFIC HEAT AT CONSTANT VOLUME
"Amount of heat energy required to raise the temperature to one mole of a gas by one kelvin at constant volume is called molar specific heat at constant volume".
It is denoted by Cv.
MATHEMATICAL EXPRESSION
D Qv = n Cv D T
OR
Cv = D Qv /n D T
Unit:J/ mole K or J/ mole-1 K-1
At constant volume all the heat supplied is fully utilized in increasing the temperature of the gas.

SPECIFIC HEAT

"Amount of heat energy required to raise the temperature of unit mass of a substance by one Kelvin or 1° C is known as specific heat of the substance."
MATHEMATICAL EXPRESSION

If D Q is the amount of heat required to raise the temperature of "m" kg of the substance through ‘D T Kelvin , Then
D Q µ m .......(i)D Q µ D T ........(ii)or D Q = m c D T
where ‘C’ is the constant called specific heat of substance.
OR
c = D Q / m D T
UNIT OF SPECIFIC HEAT
Unit of specific heat is J/kg K in S.I. system
Experiments show that specific heat of a particular material varies with temperature.Specific heat is not a precious concept for calculation because numbers of molecules per unit mass changes from material to material.
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DETERMINATION OF SPECIFIC HEAT
Specific heat of a solid substance can be determined by the "Method of Mixture" using the concept of the "law of Heat Exchange" i.e.
heat lost by hot body = heat gained by cold body
The method of mixture based on the fact that when a hot substance is mixed with a cold substance, the hot body loses heat and the cold body absorbs heat until thermal equilibrium is attained. At equilibrium, final temperature of mixture is measured. The specific heat of the substance is calculated with the help of the law of heat exchange.
Let
Mass of substance = ms kg
Mass of liquid = ml kg
Mass of calorie meter = mc kg
Initial temperature of the substance = Ts K
Initial temperature of the liquid = Tl K
Initial temperature of the calorie meter = Tc K
Specific heat of substance = Cs = ?
Specific heat of liquid = Cl
Specific heat of the material of the calorie meter = Cc
Final temperature of the mixture = T K
According to the law of heat exchange

FUNCTION

FUNCTION

Thermostat is a device which is used to maintain a desired temperature in a system like refrigerator, air-conditioner,iron and in a number of devices.
PRINCIPLE

Thermostat works on the principle of thermal expansion of solid materials.
CONSTRUCTION

A bimetallic thermostat device consists of a strip of two different metals having different coefficients of linear expansion.
The bimetallic strip works as an electric contact breaker in an electric heating circuit. The circuit is
broken when the desired temperature is reached.

Due to difference in the coefficients of linear expansion of two metals, The bimetallic strip bends in the
form of a downward curve and the circuit is broken. The metallic strip is in contact with a screw 'S'.
When it becomes hot, bends downward and contact at 'P' is broken. Thus the current stops flowing
through the heating coil. When the temperature falls, the strip contracts and the contact at 'P' is
restored.
USES
Bimetallic thermostats are widely used in numerous appliances such as refrigerator, airconditioner, Iron, ice plants etc

Main postulates of kinetic molecular theory of gases are as under

A gas consists of very small microscopic particles called 'molecules'. Depending upon the nature of gas each gas molecule may consists of an atom or group of atoms. Molecules are in a state of continuous motion.
All the molecules of a gas are in stable state and are considered identical.

Any finite volume of a gas consists of very large number of molecules. At S.T.P. there are 3 x 1025 molecules in a cubic meter.

The molecules are wide separated from each other as compared to their own dimensions.

The diameter of a molecule is about 3 x 10-10 meter.

Gas molecules move in straight line in all possible directions (random movement) with various speeds.

Gas molecules collide with each other and with the walls of container. There collisions are perfectly elastic in nature.
Gas molecules when collide with the walls of container, they transfer their momentum which appears as pressure of gas.

Molecules of an ideal gas exert no force of attraction or repulsion on one another except during collision.

The average kinetic energy of gas molecules is directly proportional to absolute temperature.

At a given temperature, the molecules of all gases have the same kinetic energy.

Newtonian mechanics is applicable to molecular motion

HEAT

Heat is a form of energy and is defined as: "The total kinetic energy of all the molecules of a body "
SYMBOL
It is denoted by "Q" or "q"
UNITS

(1) Joule(2) B.T.U(3) Calorie
CONVERSION
1 B.T.U = 251.996 Cal ( or 252 Cal)1 calorie = 4.186 Joule ( or 4.2 joule)
FLOW OF HEAT
Natural flow of heat always takes place from a region of high temperature to a region of lower temperature.
THERMOMETRIC PROPERTIES
Properties of a substance that vary uniformly with the variation in temperature are referred to as Thermometric properties. EXAMPLES:Volume , Density ,Viscosity , Pressure , Surface Tension , Area
THERMAL EQUILIBRIUM
When two bodies at different temperatures are brought into thermal contact , heat flows from hotbody to cold body till the temperature of both the bodies becomes equal .This state is referred to as THERMAL EQUILIBRIUM.
TEMPERATURE

"Average kinetic energy of the molecules of a body is called temperature."
Temperature describes the degree of hotness of a body.