Lecture 3: Heat Engines Flashcards
(16 cards)
carnot engine
an idealised, reversible heat engine of maximal efficiency operating on a working substance between two thermal reservoirs to convert heat, Q, into mechanical energy, W.
greatest efficiency comes from
greatest temperature differences – but materials melting form a practical limit.
carnot cycle breakdown
ab: isothermal heat absorption, taking heat Q1 at constant T1
bc: adiabatic expansion with no heat exchange
cd: isothermal heat loss at temperature T2 (<T1)
da: adiabatic compression with no heat exchange
cycle
a series of processes that (eventually) return a system to its initial state
heat engine
a device operating on a working substance between two thermal reservoirs to convert heat, Q, into mechanical energy, W.
heat engine process
extract heat Q1 from hot reservoir: isothermal heating
perform work W using cyclic process: isentropic work out
lose some heat, Q2, to cold reservoir: isothermal cooling
compress fluid again to return to start: isentropic work in
efficiency of engine
n = work out of engine / heat into engine
=W/Q1 = Q1-Q2/Q1 = 1-Q2/Q1
conceptual four-stage heat engine
hot body, heat in to heat exchanger
turbine - work out
heat exchanger, heat out into cold body
compressor - work in
Kelvin-Planck statement
“It is impossible to construct a device that, operating in a cycle, will produce no other effect than the conversion of heat into work.”
implications of Kelvin-Planck statement
ie. W < Q1
in essence, 100% efficiency is not possible
implications for power generators, engines, etc.
calusius statement
“It is impossible to construct a device that, operating in a cycle, produces no other effect than the transfer of heat from a colder body to a hotter body.”
implications of Clausius statement
ie. Q1, ≠ Q2 in fig to left and must have some W
from experience, heat can flow hot to cold but Clausius statement implies that the reverse isn’t spontaneous: it takes work to run a fridge
equivalence of kelvin-planck and clausius forms (1)
- Consider a heat engine that violates the Clausius statement, transferring heat Q2 from a cold body at T2 to a hot body at T1.
2.Let it run in parallel with a normal heat engine that extracts Q1 from the hot body, transfers Q2 to the cold body and does work W = Q1 - Q2.
3.The net result:extraction of heat Q1-Q2 from the hot body, no change to the cold body, work done W = Q1 – Q2.
ie claus violated –> kp violated
equivalence of KP and Claus forms (2)
1.Consider a heat engine that violates the Kelvin-Planck statement, extracting heat Q1 from a hot body at T1 to perform work W = Q1
2.Let it run in parallel with a normal heat engine (operating in reverse) that extracts Q2 from a cold body and transfers heat Q3 to the hot body.
3.Energy conservation gives Q3 = Q2+W = Q2+Q1
4.The net result is a transfer of heat from the cold body to the hot body.
both violated both ways round
carnot’s theorem
“No engine operating between two thermal reservoirs can be more efficient than a reversible engine operating between those reservoirs.”
