Equipo G
Contreras Viveros Alex----Isochoric process
Gutierrez Reyes Joel------Isobaric process
Resendiz Jiménez Omar---Isothermal process
Valtierra Jiménez ------Adiabatic process
Rojas Herrera Tania------Polytropic process
Thermodynamic process
A thermodynamic process may be defined as the energetic evolution of a thermodynamic system proceeding from an initial state to a final state. Paths through the space of thermodynamic variables are often specified by holding certain thermodynamic variables constant. It is useful to group these processes into pairs, in which each variable held constant is one member of a conjugate pair.
Isochoric Process
An isochoric process, also called an isovolumetric process, is a process during which volume remains constant. The name is derived from the Greek isos, "equal", and khora, "place."
If an ideal gas is used in an isochoric process, and the quantity of gas stays constant, then the increase in energy is proportional to an increase in temperature and pressure. Take for example a gas heated in a rigid container: the pressure and temperature of the gas will increase, but the volume will remain the same.
In the ideal Otto cycle we found an example of an isochoric process when we assume an instantaneous burning of the gasoline-air mixture in an internal combustion engine car. There is an increase in the temperature and the pressure of the gas inside the cylinder while the volume remains the same.
Equations
If the volume stays constant: (ΔV = 0), this implies that the process does no pressure-volume work, since such work is defined by:
ΔW = PΔV
where P is pressure (no minus sign; this is work done by the system).
By applying the first law of thermodynamics, we can deduce that ΔU the change in the system's internal energy, is:
ΔU = Q
for an isochoric process: all the heat being transferred to the system is added to the system's internal energy, U. If the quantity of gas stays constant, then this increase in energy is proportional to an increase in temperature,
Q = mCVΔT
where CV is molar specific heat for constant volume.
On a pressure volume diagram, an isochoric process appears as a straight vertical line. Its thermodynamic conjugate, an isobaric process would appear as a straight horizontal line.
Isochoric Process in the Pressure volume diagram. In this diagram, pressure increases, but volume remains constant.
Isobaric Process
An isobaric process is a thermodynamic process in which the pressure stays constant: Δp = 0 The term derives from the Greek isos, "equal," and barus, "heavy." The heat transferred to the system does work but also changes the internal energy of the system:
The yellow area represents the work done
According to the first law of thermodynamics, where W is work done by the system, U is internal energy, and Q is heat. Pressure-volume work (by the system) is defined as: (Δ means change over the whole process, it doesn't mean differential)
but since pressure is constant, this means that
.
Applying the ideal gas law, this becomes
assuming that the quantity of gas stays constant (e.g. no phase change during a chemical reaction). Since it is generally true that
then substituting the last two equations into the first equation produces:
.
The quantity in parentheses is equivalent to the molar specific heat for constant pressure:
cp = cV + R
and if the gas involved in the isobaric process is monatomic then and .
An isobaric process is shown on a P-V diagram as a straight horizontal line, connecting the initial and final thermostatic states. If the process moves towards the right, then it is an expansion. If the process moves towards the left, then it is a compression.
If the volume compresses (delta V = final volume - initial volume < 0), then W < 0. That is, during isobaric compression the gas does negative work, or the environment does positive work. Restated, the environment does positive work on the gas.
If the volume expands (delta V = final volume - initial volume > 0), then W > 0. That is, during isobaric expansion the gas does positive work, or equivalently, the environment does negative work. Restated, the gas does positive work on the environment.
Enthalpy. An isochoric process is described by the equation Q = ΔU. It would be convenient to have a similar equation for isobaric processes. Substituting the second equation into the first yields
The quantity U + p V is a state function so that it can be given a name. It is called enthalpy, and is denoted as H. Therefore an isobaric process can be more succinctly described as
.
Variable density viewpoint. A given quantity (mass M) of gas in a changing volume produces a change in density ρ. In this context the ideal gas law is written
R(T ρ) = M P
where T is thermodynamic temperature above absolute zero. When R and M are taken as constant, then pressure P can stay constant as the density-tempertature quadrant (ρ,T ) undergoes a squeeze mapping.
Isothermal Process
Isothermal process or isothermic process to the change of reversible temperature in a thermodynamic system is denominated, being this change of constant temperature in all the system. For a substance that carries out a change of state static and isothermally, the transferred heat can be calculated of advisable way according to the second law of the thermodynamics.
Q12 = ∫ T dS = T(S2- S1) = mT(s2-s1)…..eq. 1
Combining the previous equation with the first law of the thermodynamics, that is obtained for a closed system carries out a static change of state isothermally.
Wideal = (U1-T1S1) - (U2-T2S2)
On the other hand, of the definition of the function of Helmholtz or function of work.
A= U-TS
where: A it is work, U it is internal energy, T is temperature and S is entropy.
Reason why eq 1 can be written like:
Wideal = (A1-A2)T = -(A2-A1)T
One concludes then that the diminution in the function of Helmholtz of a system represents the maximum work that can develop that one during an isothermal process by means of some appropriate device. In the same way, the diminution in the function of Helmholtz of a system that is in an suitable device to absorb work, the minimum work necessary to carry out the process isothermally. This is the reason for which the function of Helmholtz also considers a potential function him.
An isothermal curve is a line that on a diagram represents the successive values of the diverse variables of a system in an isothermal process.
The isotherms of an ideal gas in a diagram P-V, call diagram of Clapeyron, are equilateral hyperbolas, whose equation is P•V = constant.
Example of an isothermal problem.
Two kilograms of gaseous nitrogen confined in a cylinder that lodges a piston, static carry out a change of state from 300 k and 101,325 kPa to 300 a final state to 300 k and 20.000 kPa. Heat transference can be between nitrogen and a heat deposit that is 300k.
A) It determines the work transferred by nitrogen
B) It determines the total heat transferred between nitrogen and the deposit. .
Because it is a static and isothermal work.
A) 1W2 = m[(u1-u2)T = -T(s1-s2)]….eq 1
Using data of the table of Nitrogen it is obtained:.
u1 =h1 – p1v1
= (311.163-101.325 x .8786) kJ/ Kg
= 222.138 kJ/Kg
S1 = 6.8418 kJ/Kg K
u2 = h2 – p2 v2
= (279.010 – 20,000 x 0.004704) kJ/Kg
= 184.93 kJ/Kg
s2= 5.1630 kJ/Kg
Replacing the numerical values in the equation.
1W2 = 2[ ( 222.138-184.93 ) – 300(6.8418 – 5.1630) ] kJ
= -932,864 kJ. The negative sign means that the work takes place in the gas.
Since the process static and isothermal, it is had of the second law
1Q2 = m T (s2 – s1)
= 2 x 300 (5.1630 – 6.8418) kJ
= -1007.28 kJ.
The negative sign means that the heat is extracted of the gas.
BIBLIOGRAPHI
Ingeniería termodinámica. Fundamentos y aplicaciones. Francis. F. Huang, Primera edición, México 1997. Editorial continental
Adiabatic Process
I
n thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which no heat is transferred to or from the working fluid. The term "adiabatic" literally means impassable, coming from the Greek roots ἀ- ("not"), διὰ- ("through"), and βαῖνειν ("to pass"); this etymology corresponds here to an absence of heat transfer. Conversely, a process that involves heat transfer (addition or loss of heat to the surroundings) is generally called adiabatic.
For example, an adiabatic boundary is a boundary that is impermeable to heat transfer and the system is said to be adiabatically (or thermally) insulated; an insulated wall approximates an adiabatic boundary. Another example is the adiabatic flame temperature, which is the temperature that would be achieved by a flame in the absence of heat loss to the surroundings. An adiabatic process that is reversible is also called an isentropic process. Additionally, an adiabatic process that is irreversible and extracts no work is in an isenthalpic process, such as viscous drag, progressing towards a nonnegative change in entropy.
One opposite extreme—allowing heat transfer with the surroundings, causing the temperature to remain constant—is known as an isothermal process. Since temperature is thermodynamically conjugate to entropy, the isothermal process is conjugate to the adiabatic process for reversible transformations.
A transformation of a thermodynamic system can be considered adiabatic when it is quick enough that no significant heat is transferred between the system and the outside. At the opposite extreme, a transformation of a thermodynamic system can be considered isothermal if it is slow enough so that the system's temperature remains constant by heat exchange with the outside.
Adiabatic heating occurs when the pressure of a gas is increased from work done on it by its surroundings, ie a piston. Diesel engines rely on adiabatic heating during their compression stroke to elevate the temperature sufficiently to ignite the fuel. Similarly, jet engines rely upon adiabatic heating to create the correct compression of the air to enable fuel to be injected and ignition to then occur
Adiabatic cooling occurs when the pressure of a substance is decreased as it does work on its surroundings. Adiabatic cooling does not have to involve a fluid. One technique used to reach very low temperatures (thousandths and even millionths of a degree above absolute zero) is adiabatic demagnetisation, where the change in magnetic field on a magnetic material is used to provide adiabatic cooling. Adiabatic cooling also occurs in the Earth's atmosphere with orographic lifting and lee waves, and this can form pileus or lenticular clouds if the air is cooled below the dew point.
Ideal gas (reversible case only)
For a simple substance, during an adiabatic process in which the volume increases, the internal energy of the working substance must decrease
The mathematical equation for an ideal fluid undergoing a reversible (i.e., no entropy generation) adiabatic process is
where P is pressure, V is volume, and
CP being the specific heat for constant pressure and CV being the specific heat for constant volume. α is the number of degrees of freedom divided by 2 (3/2 for monatomic gas, 5/2 for diatomic gas). For a monatomic ideal gas, γ = 5 / 3, and for a diatomic gas (such as nitrogen and oxygen, the main components of air) γ = 7 / 5. Note that the above formula is only applicable to classical ideal gases and not Bose-Einstein or Fermi gases.
For reversible adiabatic processes, it is also true that
where T is an absolute temperature.
Bibliography:
http://en.wikipedia.org/wiki/Adiabatic_process
Polytropic Process
When a gas undergoes a reversible process in which there is heat transfer, the process frequently takes place in such a manner that a plot of the Log P (pressure) vs. Log V (volume) is a straightline. Or stated in equation form PVn = a constant.
This type of process is called a polytropic process.
An example of a polytropic process is the expansion of the combustion gasses in the cylinder of a water-cooled reciprocating engine.
2- Example:Compression or Expansion of a Gas in a Real System such as a Turbine
Many processes can be approximated by the law:
where,
P= Pressure,
v= Volume,
n= an index depending on the process type.
Polytropic processes are internally reversible. Some examples are vapors and perfect gases in many non-flow processes, such as:
· n=0, results in P=constant i.e. isobaric process.
· n=infinity, results in v=constant i.e. isometric process.
· n=1, results in P v=constant, which is an isothermal process for a perfect gas.
· n=, which is a reversible adiabatic process for a perfect gas.
Some Polytropic processes are shown in figure below:
The initial state of working fluid is shown by point 0 on the P-V diagram. The polytropic state changes are:
· 0 to 1= constant pressure heating,
· 0 to 2= constant volume heating,
· 0 to 3= reversible adiabatic compression,
· 0 to 4= isothermal compression,
· 0 to 5= constant pressure cooling,
· 0 to 6= constant volume cooling,
· 0 to 7= reversible adiabatic expansion,
· 0 to 8= isothermal expansion.
polytropic process is a thermodynamic process that obeys the relation:
PVn = C,
where P is the pressure, V is volume, n is any real number (the polytropic index), and C is a constant. This equation can be used to accurately characterize processes of certain systems, notably the compression or expansion of a gas, but in some cases, possibly liquids and solids.