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The branch of physics which deals with the study of heat energy and transfer of heat into other forms of energy like mechanical energy. The world "Therm" means heat, whereas, the world "Dynamics" means motion. So we may say that we study heat in motion in the subject Thermodynamics.
Heat is the form of energy that is transferred between a system and its surrounding due to change of temperature.
Temperature means the degree of hotness or coldness of a body. Heat is denoted by symbol "Q" and has a SI Unit of "Joule". Other units of heat are calorie, BTU. Temperature is denoted by the symbol "T" and SI Unit of temperature is "k" or Kelvin, other units are Celsius "C" and Fahrenheit "F".
Kinetic Theory of Gases:
The behaviour of gases is well defined by the kinetic theory of gases which is based upon microscopic approach. The Important postulates of kinetic Energy theory are:
- A finite volume of gas has a large number of molecules.
- The size of the molecule is much smaller than the separation between them.
- The gas molecules are in random motion and may change their direction of motion.
- Due to random motion the gas molecules collide with each other and the walls of the container. The collisions are perfectly elastic.
- The pressure exerted by the gas molecules is due to their elastic collision with the walls of the container, which is formulated as:
P = 2/3 No <1/2 MV2> Or P = Constant x <KE> Or P α <KE>
Deviation of Gas Law's:
- 1Boyle's Law:According to Kinetic theory, we have:
P = 2/3 N/V < 1/2mv2 > PV = �" N <½ mv2> For a given mass of gas, "N"- No of molecules is constant. Similarly, <KE> is constant. So we may say, PV = Constant Or P α 1/v Which is the statement of "Boyle's Law".Advertisement
- 2Charles Law:From kinetic theory of gasses, we say:
V = �" N/p <½ mV2> For a given mass "N' is constant. If pressure is kept constant then N/P is constant, so: V = Constant <½ mv 2> As <½ mv2> α T, Hence, V α T, or "v/1 = Constant" which is Charles Law
The sum of all forms of energies of molecules (Kinetic and potential) of a substance is termed as Internal energy. It is denoted by symbol "You" and SI Unit is "Joule".
The study of thermodynamics, usually ideal gas is considered as a working substance. The molecules of ideal gas are mere mass points which exert no forces on each other. So the internal energy of the gas system is generally the translational KE of its molecules.
- Changes of Internal energy:
Change in Internal energy is represented by "ΔYou". ΔYou is taken positive when internal energy increases and taken negative when Internal energy decreases.
- As a state variable:
In thermodynamic Internal energy is a function of state (State variable). Consequently, It does not depend on the path but depends on initial and final states of a system.
Work and Heat
Both work and heat are similar in the transfer of energy by some means. The Idea was first applied to the steam engine where it was natural to transfer "Heat in" and get "Work out". So both work and heat are defined as positive quantities.
- Sign Convention:
- 1Work done by the system is positive.
- 2Work done by the system on the environment is positive.
- 3Heat entering the system is positive.
- 4Heat leaving the system is negative.
Law's of Thermodynamics:
The general principles which deal with heat energy and its transformation into mechanical energy are called the Law's of thermodynamics.
- First Law of Thermodynamics:
Statement: "In any thermodynamic process when heat ΔQ is added to a system, this energy appears as an increase in Internal energy "ΔYou" of system and work done by the system on its "Environment or Surroundings".
Explanation: When heat is added to the system, there is an Increase in Internal energy due to rise is temperature, an Increase in pressure or change occurs. If at the same time, a substance is allowed to do work on its surroundings by expansion then we may say,
The rate of change of heat = Rate of change of internal energy + Work done. ΔQ = (You2 - You1) + Δw
But ΔYou = You2 - You1 ΔQ = ΔYou + Δw Which is mathematical form of first law of thermodynamics.
- The Bicycle pump:
A bicycle pump provides a good example of the first law of thermodynamics. When we pump the handle rapidly, it becomes hot due to mechanical work done on the gas, raising thereby its internal energy, which is shown by increasing in temperature:
By first law: -Δw = ΔYou - ΔQ Or ΔQ = ΔYou + Δw
- Human metabolism:
Human metabolism also provides an example of energy conservation, since the first law is also known to be another form of the law of conservation of energy. Human beings and other animals do work when they walk, Runs or move objects. Work requires energy. Energy is also needed for growth to make new cells and to replace the old cells that have died. "Energy transforming process that occurs with an organism are named as the metabolism". We can apply first law of thermodynamics here as
ΔYou = ΔQ - Δw.
Applications of the first law of thermodynamics:
- Isothermal process:
It is a process which is carried out at constant temperature"
Let us consider a cylinder filled with a non-conducting walls, non-conducting and frictionless piston and a base is conducting. A gas is enclosed in it. It is placed on a heat reservoir, which is a source of large heat capacity, at some temperature "T". This system fulfills the condition for the application of Boyle's law. Therefore, When a gas expands or compresses isothermally, the product of its pressure and volume during the process remains constant. If P1, V1, are initial pressure and volume. Whereas, P2V2, are pressure and volume after the isothermal change takes place. Then, P1V1 = P2V2 . In case of an ideal gas, the PE associated with its molecules is zero, Hence internal energy of ideal gas depends upon its temperature. So In this case,
ΔYou = O Then by first law: ΔQ = ΔW + ΔYou ΔQ = ΔW + O ΔQ = ΔW.
- Adiabatic process:
"An adiabatic process is one in which no heat enters or leaves the system."
For an adiabatic process, the prevention of heat flow may be done either by surrounding of a system with a thick layer of heat insulating material, such as cork, asbestos styrofoam etc, or by performing the process quickly. Adiabatic change occurs when the gas expands or is compressed rapidly, the examples of adiabatic process are:
- The rapid escape air from a burot type.
- Passage of sounds through air.
- Cloud formation in the atmosphere.
There are two types of adiabatic process, as seen from the formula, ΔQ = ΔYou + ΔW under condition, "ΔQ = O", we have, O = ΔYou + ΔW
- 1ΔW = -ΔYou (Adiabatic expansion).
- 2ΔYou = - ΔW (Adiabatic compression).Advertisement
Molar specific heat of a gas
"It is the amount of heat required to one mole of the substance through 1K (Kelvin)."
We begin the topic with the definitions of molar specific heat in two ways.
- Molar specific heat at constant volume:
"It is the amount of heat transfer required to raise the temperature of one mole of a gas through one 1K (kelvin) at constant volume.
Mathematically, ΔQ α Cv ΔT ΔQ = 1CvΔT ΔQ = CvΔT
Now according to first law, ΔQv = ΔW + ΔYou but ΔW = 0, ΔQv = ΔYou ΔYou = Cv ΔT
- Molar specific heat at constant pressure:
"It is the amount of heat transfer required to raise the temperature of one mole of gas up to one kelvin (1K), at constant pressure."
Mathematically, ΔQp = (1)CpΔT Δ Qp = Cp ΔT
To prove: Cp - Cv = R As, ΔYou = Cv ΔT →1 ΔW = PΔV ΔQp = ΔYou + ΔW ΔQp = CvΔT + PΔV ΔQ = CvΔT + RΔT CpΔT = CvΔT - RΔT (Cp - Cv)
ΔT= R ΔTCp - Cv = R
- Reversible process:
"A reversible process is the one which can be retraced in exactly reverse order, without producing any change in the surrounding."
- Reversible cycle
"A succession of events which bring the system back to its initial condition is called a cycle. A reversible cycle is the one in which all the changes are reversible."
- Irreversible process:
"If a process can not be retraced in the backward direction by reversing the controlling factors, it is an irreversible process."
Second Law of Thermodynamics
Second law of thermodynamics can be explained as, According to "Lord Kelvin's statement which is based on the working of a heat engine, the second law is defined as, "It is impossible to construct such a device that may convert heat, extracted from a single reservoir into work done entirely without any change in the working system".
Another statement is given by "Clausius" is, " It is impossible to cause beat to flow from a cold body to a hot body without the expenditure of external work".
" In 1940's "Sadi Carnot" described the ideal engine is free from friction and heat losses."
It works on the principle of any cyclic heat engine and its cycle is called Carnot cycle.
Carnot engine consists of a cylinder filled with non-conducting walls, non-conducting and frictionless piston, and a conducting base. An Ideal gas is used as a working substance.
A Carnot cycle can be explained as:
- The gas is allowed to expand isothermally at temperature T1, absorbing heat Q1 from HTR.
- The gas is allowed to expand adiabatically to temperature T2.
- The gas compressed isothermally at temp T2, rejected heat Q2 to LTR.
- Finally the gas is compressed adiabatically to restore its initial state at temperature T1.
"The network done during one cycle equals to the area enclosed by path."
ABCDA of the Pv diagram:
δQ = δYou + δW δQ = δW δW = Q1 - Q2
Efficiency = Output (work) / Input(Energy)
η = Q1 - Q2 / Q1 = Q1 /Q1 - Q2 / Q1 η = 1 - Q2 / Q1
η % = (1 - Q2/Q1 ) x 100
In terms of temperature,
η % = (1-T2 / T1) x 100
"The measure of the disorder of a system is called entropy." Or "Measure of unavailability of energy is called entropy."
Concept was given by R-clausius in 1856,
Mathematically, δS = δ / T
S.I. Unit of Entropy is Joule per Kelvin (J/K).
Referencing this Article
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Categories : Physics
Recent edits by: Jen Moreau, TheGuyLoveNY