Download Lecture 14 - UMD Physics

Lecture 14
• Interaction of 2 systems at different
temperatures
• Irreversible processes: 2nd Law of
Thermodynamics
• Chapter 19: Heat Engines and Refrigerators
Thermal interactions
• T’s change via collisions at boundary (not mechanical
interaction)
Etot = E1i + E2i constant with
3
3
E1i = 2 n1 RT1i and E2i = 2 n2 RT2i
• elastic collision (total energy conserved): energy
transfer from faster atom to slower atom
• on average, energy transferred from 1 to 2 ( T
1i
> T2i )
Equilibrium
E1f
N1
E1f
=
=
E2f
Etot
=
N2
N1 +N2 ⇒
N1
N2
E
;
E
=
2f
N1 +N2 tot
N1 +N2 Etot
W = 0 (barrier does not move) ⇒ 1st law gives
Q1 = ∆E1 = E1f − E1i ; Q2 = ∆E2 = E2f − E2i
and Q1 = −Q2 (energy conservation)
• 2 systems reach
common final T due to
energy exchange via
atomic collisions (in
reality via wall, but still
no mechanical
interaction)
Example
• 2.0 g of helium at an initial temperature of 300 K
interacts thermally with 8.0 g of oxygen at an initial
temperature of 600 K.
(a) What is the initial thermal energy of each gas?
(b) What is the final thermal energy of each gas
(c) How much heat is transferred, and in which
direction?
(d) What is the final temperature?
Irreversible processes
• heat not transferred cold to hot (conserves energy)
• reversible microscopic (molecular) motions
irreversible macroscopic phenomena? New law
(past vs. future)
Statistics of (Very) Large Numbers
• small probability for 1Nto= 10
increase, especially if
1
20
• net result of many collisions is to transfer energy
from 1 to 2
• equilibrium state is most probable
2nd Law of Thermodynamics
•
negligible probability (not impossible) for atoms to spontaneously
order: more random arrangements...
•
state variable entropy: probability for macroscopic state to
occur (measures disorder)
•
•
2 systems with different T’s: lower entropy (more order) than...
•
order turns into disorder;information lost; “system runs
down” (vastly more random states: laws of probability)
•
•
informally (i): heat transferred from hotter to colder
formally: entropy of isolated system never decreases (can order
by reaching from outside e.g. refrigerator for cold to hot)
informally (ii): irreversible evolution from less-likely to more-likely
macroscopic state gives time direction (entropy increases is
“future”)
Chapter 19
• physical principles for all heat engines (transform heat
energy into work) and refrigerators (uses work to
move heat from cold to hot)
• 2nd law: limit on efficiency (Carnot cycle)
Today
• general concepts of turning heat into work; heat
engines and refrigerators
Heat
Work
•
thermodynamics: transformation of energy e.g. heat into work
obeys (i)1st law (energy conservation): ∆Eth = W + Q
(ii) 2nd law: heat flows from hotter to colder (spontaneously)
•
Work done by system, Ws (vs. work done on system by external
force, W: heat and work are 2 ways to transfer energy to system)
equilibrium: F̄gas = −F̄ext ⇒ Ws = −W = the area under the pV curve
Ws > 0 (W < 0) during expansion (energy transferred out of system)
1st law: Q = Ws + ∆Eth (heat used to do work or stored as thermal)
Energy Transfer diagrams
•
energy reservoir (hot or cold): much larger than system,
temperature does not change when heat transferred between it
and system due to difference in temperatures
QH, C (> 0) = heat transferred to/from a hot/cold reservoir
Q = −QC in 1st law (heat transferred from system...)
1st law: Q = Ws + ∆Eth refers to system
Q = QH − QC ; Ws = 0; ∆Eth = 0 (steady state) ⇒
QH = QC (system provides route for energy transfer from hot to cold)
heat transferred from cold to hot: 1st law not violated if QH = QC ,
but 2nd law does not allow spontaneous transfer...
•
Efficiency of Heat
Work
Work into heat
100 % efficient: e.g. warm up rocks
from ocean by rubbing (W → ∆Eth);
back into ocean ( ∆Eth → QC );
continue as long as there is motion
Heat into Work
•
isothermal expansion: 100%
efficient, but one-time process
(piston reaches end of cylinder)
•
practical device must return to
initial state for continued use, but
2nd law does not allow perfect
engine (100% efficient): asymmetry
of 2 conversions similar to heat
transfer
•
Heat engines
closed cycle device (e.g. car engine: p, T
inside cylinder repeated) extracts heat
(combustion of fuel); does useful work
(move pistons...); exhausts heat
(radiator...): all state variables return to
initial once every cycle
(∆Eth )net = 0 (over 1 full cycle)
1st law: (∆Eth )net = Qnet − Wout
with Qnet = QH − QC ⇒
•
•
(energy
conservation)
thermal efficiency
=1−
QC
QH
perfect engine (η = 1) not possible:
must exhaust energy (waste heat:
energy extracted from hot reservoir, not transformed into work)
A Heat-Engine Example
•
useful work of lifting mass during
isobaric expansion...step (e): no net
change in gas (start lifting mass again)
•
•
heat engines require source and sink
reservoirs not explicitly shown: TH >
highest system temperature; TC <
coldest...