Table Of ContentFirst Law –Processes in Closed Systems
A process occurs when a system’s state (as measured by its properties)
changes for any reason. Processes may be reversible, or actual (irreversible).
In this context the word ‘reversible’has a special meaning.
A reversible process is one which is wholly theoretical, but can be imagined as
one which occurs without incurring friction, turbulence, leakageor anything
which causes unrecoverable energy losses.
All of the processes we are going to study at this stage will beconsidered to be
reversible.
We will deal with actual (real or practical) processes later (THER205).
Processes may occur in particular ways:
This may be because we deliberately ‘arrange’it to be so,
or as a ‘natural consequence’of the way it is carried out.
at constant temperature : isothermal
at constant pressure : isobaric
at constant volume : isochoric
at constant enthalpy : isenthalpic
at constant entropy : isentropic
with no heat transfer to the surroundings : adiabatic
Heat transfer to/from a perfect gas (closed system) keeping the volume constant
2
e
ur
s
s
e
pr
1
volume
Heat transfer in
As we would expect the temperature and pressure rises,
but because there is no change in volume no work is done.
From the First Law: Q =DDDDU
If the heat transfer was outof the gas the temperature and
pressure would fall, and no work would be done.
1
Heat transfer at constant volume (closed system)
Heat can be transferred to(often called a heating process) or from(called a cooling
process) a gas at constant volume(isochorically).
The process is described by: V = c o n s t and the properties are related by:
pV =mRT
Since the volume remains constantthere is no work transfer:
W =0
12
therefore the only effect of the heat transfer is to raise the internal energy level.
Q = DU
12
From calorimetry the heat transfer required to change the temperature by a
given amount is given by: Q = m c DT
12 v
where c is the specific heat capacity of the gas at constant volume.
v
For a perfect gas the internal energy is dependent ONLY on temperature*,
so we can write:
DU = m c DT
v
Irrespective of how a temperature change may occur, this will always be true.
*Joule’s Law
Heat transfer to/from a perfect gas (closed system) keeping the pressure constant
1 2
e
ur
s
s
e
pr
volume
Heat transferin
As we would expect the temperature and volume increases
and work is done by the system. W = -p (V -V )
12 2 1
From the First Law: Q + W =DDDDU
If the heat transfer was outof the system the temperature and
volume would decrease, and the work transfer would be positive.
2
Heat transfer at constant pressure (closed system)
Heat can be transferred to (often called a heating process) or from (called a cooling
process) a gas at constant pressure(isobarically).
The process is described by: p = c o n s t and the properties are related by:
pV =mRT
Since the volume changesthere is work transfer:
W = -p(V -V )
12 2 1
From the First Law:
Q = DU -W = DU + p(V -V )
12 12 2 1
since pV =mRT p(V2 -V1) = mR(T2 -T1)
and DU=m c DT \ Q =m c DT+m R DT =m (c +R)DT
v 12 v v
Since c and Rare characteristics of the gas and remain approximately constant
v
for moderate temperature ranges we combine them to obtain the specific heat
capacity of the gas at constant pressure c . c =c +R
p p v
The heat transfer at constant pressure is given by: Q =m c DT
12 p
Work transfer into a perfect gas (closed system)
2
As we would expect the
e pressure rises, but what
ur
s happens to the temperature?
s
e
pr
1
volume
3
Work transfer into a perfect gas (closed system)
2 Our normal experience of
compressing a gas is that its
temperature rises.
(e.g. a bicycle pump).
e
ur
s
s
e This is because we normally
pr carry out the compression
process relatively quickly
and the ‘heat’does not have
1 time to escape.
volume
Adiabatic Work transfer into a perfect gas (closed system)
2 If we carry out the process
very quickly or ensure that it is
pVg =const perfectly insulated then no
e
ur heat will escape at all………
s
s an ADIABATICprocess.
e
pr
The processis defined by:
pVg =const
1 pVg = p V g
1 1 2 2
volume
c
g is known as the adiabatic index of a gas. It can be shown that (cid:1)= p
c
v
4
Isothermal work transfer into a perfect gas (closed system)
If we carried out the process
very veryslowly or ensured that
the energy supplied (by work
transfer) is removed (by heat
2 pV =const transfer) at the same rate that it
is supplied, then there will be
e no net internal energy change
ur
s in the gas and hence no
s
e temperature change…an
pr
ISOTHERMALprocess
The processis defined by:
1 T =const or pV =const
pV = p V
1 1 2 2
volume
When work is transferred toa gas (often referred to as a compression process) its
volume decreases and its pressure increases. Its temperature mayincrease or remain
the same depending on whether we allow heat transfer or not.
We often illustrate such processes on a pressure/volume graph.
pVg =const adiabatic
2
pVn =const
polytropic
2
e pV =const isothermal
ur
s
s
e
pr
1
volume
If the heat transfer (out) exactly equals the work transfer (in)there is no net energy
change and the compression occurs without the temperature rising(an isothermal
process). In practice, the actual process tend to lie between the two –called polytropic.
5
Calculation of Work transfer into a perfect gas (closed system)
F
The work done dWby
force Fmoving an
dx infinitesimal distance dx
2 is given by: dW =Fdx
but F = pA
\ dW = pAdx
e
ur but Adx = -dV
s
s
e \ dW =-pdV
pr
V
2
or W =-(cid:1) pdV
12
1
V
1
2
W =-(cid:1) pdV
12
volume
1
the area under the p-V graph
Work transfer outof a perfect gas (closed system)
1
As we would expect the
e pressure falls, but what
ur
s happens to the temperature?
s
e
pr
2
volume
6
Work transfer outof a perfect gas (closed system)
Our normal experience of
1 expanding a gas is that its
temperature falls.
(e.g. letting the air out of a tire).
e
ur
ss This is because we normally
e
pr carry out the expansion
process relatively quickly and
the gas does not have time to
absorb ‘heat’from the
2 surroundings.
volume
Adiabatic work transfer outof a perfect gas (closed system)
1
If we carry out the process
very quickly or ensure that it is
e perfectly insulated then no
ur
s heat will enter at all………
s
e an ADIABATICprocess.
pr
The processis defined by:
pVg =const
2
pVg = p V g
1 1 2 2
volume
7
Isothermal work transfer outof a perfect gas (closed system)
If we carried out the process
very veryslowly or ensured that
1 the energy obtained (by work
pV =const transfer) is replaced (by heat
transfer) at the same rate that it
ure is obtained, then there will be
s no net internal energy change
s
e in the gas and hence no
pr
temperature change…an
ISOTHERMALprocess
The processis defined by:
2
T =const or pV =const
pV = p V
volume 1 1 2 2
When work is transferred froma gas (often referred to as a expansion process) its
volume increases and its pressure decreases. Its temperature maydecrease or remain
the same depending on whether we allow heat transfer or not.
We often illustrate such processes on a pressure/volume graph.
1 pVg =const adiabatic
pVn =const polytropic
pV =const isothermal
e
ur
s
s
e
pr 2
2
volume
If the heat transfer (in) exactly equals the work transfer (out)there is no net energy
change and the expansion occurs without the temperature falling (an isothermal
process). In practice, the actual process tend to lie between the two –called polytropic.
8
Calculation of Work transfer outof a perfect gas (closed system)
F
The work done dWby
force Fmoving an
1
infinitesimal distance dx
is given by: dW =Fdx
and using exactly the
e
ur same procedure as for
s
s compression we can
e
pr show that:
2
W =-(cid:1) pdV
12
2
1
volume
the area under the p-V graph
Summary –Adiabatic Processes (closed system)
If there is noheat transfer (an adiabaticprocess) the temperature changes because the
work transfer increases or decreases the internal energy.
In practice, this may be closely achieved by carrying out the process very rapidly -giving
no time for heat transfer to occur, or by ensuring the system isvery well insulated.
During a reversible adiabatic work transfer process the pressureand volume are related
by:
pVg = const and the properties are related by: pV =mRT
ggggis a characteristic of the gas known as the adiabatic index
-it may be looked up in tables.
2 2 1
W =-(cid:1) pdV =-(cid:1)const·V-gdV =- [constV 1-g-constV1-g]
12 1-g 2 1
1 1
1 p V - pV
=- [p VgV 1-g- pVgV1-g]= 2 2 1 1
1-g 2 2 2 1 1 1 g-1
The work transfer during an adiabatic p V - pV
W = 2 2 1 1
compression or expansion process is 12 g-1
given by:
9
Summary –Isothermal Processes (closed system)
If there is notemperature change (an isothermalprocess) the temperature remains
constant because the work transfer into or outof the system is exactly offset by the
heat transfer outof or into the system and therefore there is no change in internal
energy of the system. In practice, this may be closely achieved either by carrying out the
process very veryslowly -giving time for heat transfer to occur, and/or ensuring the
system can easily transfer heat to/from the surroundings.
During a reversible isothermal work transfer process the temperature remains constant:
T =const and the properties are related by: pV =mRT
2 2 mRT 2 dV
W =-(cid:1) pdV =-(cid:1) dV =-mRT(cid:1) =-mRT[lnV -lnV ]
12 V V 2 1
1 1 1
V V
=-mRTln 2 = pV ln 1
V 1 1 V
1 2
The work transfer during an isothermal V
W = pV ln 1
compression or expansion process is 12 1 1 V
given by: 2
Summary –Polytropic Processes (closed system)
In practice because many compression and expansion processes arecarried out very
rapidly they can be reasonably approximated by an adiabatic process. When
compressing a gas there is an advantage in trying to cool the process. However, it is
difficult to obtain an actual isothermal process –so the process ends up somewhere
between an isothermal process and an adiabatic process. The process is called a
polytropic process. During a reversible polytropic work transfer process the pressure
and volume are related by:
pVn = const and the properties are related by: pV =mRT
nis a known as the polytropic index –and depends on how exactly the process is
carried out –it typically has to be found by experiment.
2 2 1
W =-(cid:1) pdV =-(cid:1)const·V-ndV =- [constV 1-n -constV1-n]
12 1-g 2 1
1 1
1 p V - pV
=- [p VnV 1-n - pVnV1-n]= 2 2 1 1
1-g 2 2 2 1 1 1 n-1
The work transfer during a polytropic p V - pV
compression or expansion process is W = 2 2 1 1
12 n-1
given by:
10
