Transcript thermodynamics - Portal UniMAP

THERMODYNAMICS
Group Carnot
on
Work and Thermodynamics Process
Work, i.e. "weight lifted through a height",
was originally defined in 1824 by Sadi Carnot
“ We use here motive power (work) to express the useful effect
that a motor is capable of producing. This effect can always be
likened to the elevation of a weight to a certain height. It has, as
we know, as a measure, the product of the weight multiplied by
the height to which it is raised.”
Sadi Carnot (1796-1832):
The "father" of thermodynamics
WORK
• In thermodynamics, work is performed whenever a force
acts through a distance.
• By definition, WORK is given by the equation :
dW  Fdl
• By convention, where F is the component of force acting
along the line of the displacement dl.
• Work regarded as +ve when the displacement is in the
same direction –ve when the displacement is in the
opposite direction.
• In SI, work is measured in joules (J).
• Pressure-volume work
• Chemical thermodynamics studies PV
work, which occurs when the volume of a
fluid changes. PV work is represented by
the following differential equation:
• where:
– W = work done on the system
– P = external pressure
– V = volume
• Therefore, we have:
• A common type of work associated with a
chemical process is the work done by a gas
through expansion or the work done to a gas
through compression.
• An example,Combustion of gasoline is used to
expand gases in the cylinders of car's engine
and push back the pistons. This motion is then
translated into the motion of the car.
• Now remember that work is defined as a Force
applied over a distance is
– Work = F x Δh,
• where Δh = hfinal - hinitial.
• Thus, the work associated with moving a piston
a distance Δh is
– Work = p x ΔV,
• where ΔV = Vfinal – Vinitial,recognizing A x Δh
as the change in volume of the cylinder, so
– |Work| = p x ΔV.
• If ΔV is positive then the gas is expanding and
doing work on the surroundings. So work should
be negative
• Work = - p x ΔV
CP:
Molar Heat Capacity at constant pressure.
CV:
Molar Heat Capacity at constant volume.
CS:
Specific Heat Capacity at constant pressure.
Thermodynamic process
• can be defined as the energetic evolution of a
thermodynamic system proceeding from an initial
state to a final state.
• pressure-volume is concerned with the transfer of
mechanical or dynamic energy as the result of work.
• The basic properties are:
–
–
–
–
–
–
–
isobaric process
isochoric process
isothermal process
adiabatic process
isentropic process
isenthalpic process
steady state
Isobaric Process
• Occurs at constant pressure
• 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:
• but since pressure is constant, this means that
• Applying the ideal gas law ( PV  nRT ) , 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
•
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.
• The yellow area represents the work done
Isochoric Process
• called an isometric process or an isovolumetric
process, is a thermodynamic process in which 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 = nCVΔT
• where CV is molar specific heat for constant volume.
• On a P-V diagram, an isochoric process appears as a
straight vertical line.
Isothermal Process
• Occurs at a constant temperature: ΔT = 0
• This typically occurs when a system is in contact with an
outside thermal reservoir (heat bath), and processes
occur slowly enough to allow the system to continually
adjust to the temperature of the reservoir through heat
exchange.
• Consider an ideal gas, in which the temperature
depends only on the internal energy, which is a function
of the mean translational kinetic energy of the
molecules, as given by a Boltzmann distribution; if the
internal energy is constant, so is the temperature. Take
the number of moles n as a constant.
• but this means, according to the ideal gas law, that
• so that
• where Pi and Vi are the pressure and volume of the
initial state, Pf and Vf are the pressure and volume of
the final state, and the variables P and V stand for the
pressure and volume of any intermediate state during
an isothermal process.
• Some isotherms of an ideal gas
• Curves called isotherms appear as a hyperbolas on a PV (pressure-volume) diagram (T = constant). Each one
asymptotically approaches both the V (abscissa) and P
(ordinate) axes. This corresponds to a one-parameter
family of curves, a function of T, whose equation is
• By the first law of thermodynamics, the isotherms of an
ideal gas are also determined by the condition that
• where W is work done on the system. (While Q and W are
incremental quantities, they do not represent differentials of state
functions.) This means that, during an isothermal process, all heat
accepted by the system from its surroundings must have its energy
entirely converted to work which it performs on the surroundings.
That is, all the energy which comes into the system comes back out;
the internal energy and thus the temperature of the system remain
constant.
• The yellow area equals work.
• In a minute process of this process, the minute work dW can be
shown as follow.
dW = Fdx = PSdx = PdV
• Therefore the entire work of the process from A to B is shown with
the integration of the previous equation.
• Here, by the ideal gas equation,
• Therefore in the isothermal process, the following equation is formed.
Adiabatic Process
• Process in which there is no energy added or subtracted
from the system by heating or cooling.
• For a reversible process, this is identical to an isentropic
process.
• If the system is thermally insulated from its
environment, its boundary is a thermal insulator.
• But if a system has an entropy which has not yet
reached its maximum equilibrium value, the entropy will
increase even though the system is thermally insulated.
• An example of an adiabatic process is a gas expanding
so quickly that no heat can be transferred. The
expansion does work, and the temperature drops. This is
exactly what happens with a carbon dioxide fire
extinguisher, with the gas coming out at high pressure
and cooling as it expands at atmospheric pressure.
Isentropic Process
• Occurs at a constant entropy.
• For a reversible process this is identical to
an adiabatic process.
• If a system has an entropy which has not
yet reached its maximum equilibrium
value, a process of cooling may be
required to maintain that value of entropy.
Isenthalpic Process
• the thermodynamic potentials may be held
constant during a process which means no
change in enthalpy in the system.
Steady state
• Steady state is a more general situation than Dynamic equilibrium. If
a system is in steady state then the recently observed behaviors of
the system will continue into the future. In stochastic systems, the
probabilities that various different states will be repeated will remain
constant.
• In many systems, steady state is not achieved until some time has
elapsed after the system is started or initiated. This initial situation is
often identified as a transient state, start-up or warm-up period.
• While a dynamic equilibrium occurs when two or more reversible
processes occur at the same rate, and such a system can be said to
be in steady state; a system that is in steady state may not
necessarily be in a state of dynamic equilibrium, because some of
the processes involved are not reversible.