Thermodynamics. Definitions Thermodynamics is the study of processes in which energy is transferred...
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Transcript of Thermodynamics. Definitions Thermodynamics is the study of processes in which energy is transferred...
Thermodynamics
Definitions• Thermodynamics is the study of processes in
which energy is transferred as work and heat• The system is a set of particles we wish to study• The environment is everything else• Heat (Q) is the transfer of energy into or out of
the system by a temperature difference• Work (W) is the transfer of energy into or out of
the system by a force• Internal energy (U) is the sum of the kinetic and
potential energies of all the particles in the system
Diagram
• This diagram summarizes these concepts:
SystemHeat, Q Work, W
U
Environment
SystemBoundary
Types of Systems
• An open system allows mass and energy to enter or leave
• A closed system does not allow mass to enter or leave (but energy can)
• An isolated system does not allow energy (in any form) to enter or leave
First Law of Thermodynamics• Let Q be positive when heat is absorbed by the
system• Let W be positive when the system does work on
the environment• The first law of thermodynamics says that for a
closed system:U = Q W
SystemW
UQ
Understanding the First Law• There are only two ways for energy to transfer
into or out of a closed system: heat and work• The first law is a statement of conservation of
energy• Note that the sign of Q and W depend on the
direction of energy transfer:Signs of Q and W for a System
Q > 0 Energy added to system as heat
Q < 0 Energy removed from system as heat
Q = 0 No transfer of energy as heat
W > 0 Work done by system (expansion of gas)
W < 0 Work done on system (compression of gas)
W = 0 No work done
Example
Q: What is the change in the internal energy of a gas that releases 489 J of heat while simul-taneously being compressed by 731 J of work?
A: U = ? Q = -489 J, W = -731 JU = Q W = (-489 J) (-731 J)
= 242 J
GasU = 242 J
W = -731 J
Q = -489 J
Gases and the First Law• The first law allows us to study processes
involving gases• An ideal gas has the following state variables:
• Pressure is defined as force per area:P = F/A (SI unit: 1 Pa = 1 N/m2)
variable name units
P pressure Pa (= N/m2)V volume m3 T temperature K
n # of moles molU internal energy J
P-V Diagrams• A pressure-volume diagram lets us track the
state of a gas as it goes through a processpr
essu
re (P
a)
volume (m3)
Initial state
final state
(Pi, Vi)
(Pf, Vf)
• Pressure and volume specify the entire state of a gas under the following conditions:– gas is ideal and has the following state equation:
PV = nRT [R = 8.314 J/(molK)]– gas does not change phase nor undergo reaction
U = (constant) T– system is closed so that
n = constant• A P-V diagram lets us track the state of a gas as
energy is transferred as heat and work
Types of Thermodynamic Processes• A gas undergoing an isobaric process is at
constant pressure
The work done by the gas is W = PVU = Q PV
pres
sure
(Pa)
volume (m3)
(P,Vi) (P,Vf)
T1
T2
T3
• A gas undergoing an isovolumetric process is at constant volume
W = 0U = Q
pres
sure
(Pa)
volume (m3)
(Pf, V)
T1
T2
T3
(Pi, V)
• A gas undergoing an isothermal process is at constant temperature
U = 0 Q = W
pres
sure
(Pa)
volume (m3)T1
T2
T3
isotherms
• A gas undergoing an adiabatic process does not absorb or release any heat (Q = 0)
Q = 0U = -W
pres
sure
(Pa)
volume (m3)T1
T2
T3
Cyclic Processes• A cyclic process is one where the system
returns to its initial state after going through a series of changes in P, V, T, etc.– In the process of going through this cycle, the
system may transfer energy as heat and work– The change in internal energy for one cycle is zero
(Unet = 0)
• There are two classes of cyclic processes:– heat engines (use heat to produce work)– Refrigerators (use work to move heat from a cold
reservoir to a hotter one)
Heat Engines• The P-V diagram for a heat engine looks like this
• The process is clockwise• The work done by the system is proportional to the
area of the “eye”
pres
sure
(Pa)
volume (m3)T1
T2
T3H
eat i
n
Hea
t out
Heat from a high-temperature source (QH)
Waste heat transferred to a low-temperature reservoir (QL)
• Since Unet = 0 and Qnet = QH QL we have
Unet = Qnet Wnet
0 = Qnet Wnet
0 = QH QL Wnet
Wnet = QH QL • This diagram shows the energy flow for a heat engine:
Hot Source (TH)
Cold Sink (TL)
QL
QH
WnetHeat Engine
Efficiency of a Heat Engine• The efficiency of a heat engine is a measure of
how well the engine operates• The efficiency of a heat engine is defined as
eff = Wnet/QH
• This can be written as
eff = = 1 QH QL
QH
QL
QH
• Example:A steam engine takes in 2.25 × 104 kJ from the
boiler and gives up 1.92 × 104 kJ in exhaust every cycle.
a)How much work does the engine do every cycle?
Wnet = QH QL = 2.25 × 104 kJ 1.92 × 104 kJ
= 3.3 × 103 kJ b)What is the efficiency of the engine?eff = 1 QL /QH = 1 1.92 × 104 kJ / 2.25 × 104 kJ
= 0.15 or 15%
Second Law of ThermodynamicsAll the king’s horses and all the king’s men
Couldn’t put Humpty together again
• Many processes go only in one direction and cannot be reversed. Why?
• Even if the first law of thermodynamics is obeyed, certain things are never seen to happen:
ONE WAY
Shake-shake
– Heat is never observed to flow spontaneously from cold things to hot ones
– Broken coffee cups are never seen to spontaneously re-assemble and fly back up on the table
– Salt and pepper, once mixed, will never separate back into two layers of salt and pepper by shaking
HEAT
cold hot
Statements of the Second Law • There are many ways to state the second law of
thermodynamics, but the general idea is this:In all processes, a system tends to move from order to disorder and, in fact, the total disorder of the universe is always increasing
• What is the state of maximum disorder for an isolated system?– thermal equilibrium!
Isolated gas
T1 T2
More Order
T
Less Order (Thermal Equilibrium)
• A thermodynamic quantity called entropy is a measure of the disorder of a system
• A more scientific way of stating the second law is:In all processes, the entropy of a system tends to increase with time and, in fact the entropy of the universe is constantly increasing
• The second law can be understood in terms of probability: disordered states are far more numerous than ordered ones, and thus are far more likely to exist
The Second Law for Heat Engines
• The second law, when applied to heat engines, puts limits on their efficiency
• In fact the second law can be stated in terms of heat engines:No heat engine can be 100% efficient. In other words, the efficiency is always less than one, and the “waste heat”, QL , is never zero
• In equations:eff < 1 (never equal)QL > 0 (never equal)