Section 2: Second Law Flashcards
(63 cards)
second law of thermodynamics
ΔS> or =0
concept of entropy and second law derive historically from
heat engines
the carnot engine represents an
idealised, reversible heat engine of maximal efficiency operating on a working substance between two thermal reservoirs to convert Q into W
the greatest efficiency comes from
the greatest temperature differences, but materials melting form a practical limit
the carnot cycle comprises of
two isotherms and two (reversible) adiabatics
1-2: isothermal heat absorption
2-3: adiabatic expansion
3-4: isothermal heat loss
4-1: adiabatic compression
carnot cycle is unique in that it is the only
thermodynamic cycle operating reversibly between only two resevoris
cycle
a series of processes that eventually return a system to its initial state
heat engine
device operating on a working substance between two thermal reservoirs to convert heat Q into mechanical energy W
heat engine steps
- extract heat Q1 from hot reservoir (isothermal heating)
- perform work W under cyclic process (isentropic work out)
- lose some heat Q2 to cold reservoir (isothermal cooling)
- compress fluid again and return to start (isentropic work in)
reversing all the arrows and the sense of rotation of an engine turns
heat engine into a refrigerator
efficiency
ratio between energy out and heat in
=W/Q = Q1-Q2/Q1 = 1-Q2/Q1
can also define an efficiency for a refrigerator but in that case, we would like to
extract heat by putting work in which will give rise to a different reciprocal ratio
it is not possible to build a
perfect carnot engine
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
Clausius 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
equivalence of Kelvin-Planck and Clausius statements can be seen by
considering an engine which violates one formulation and then show that this engine would also violate the other
equivalence
consider a heat engine that violates Clausius, transferring heat Q2 from a cold body at T2 to warm body T1
let it run parallel with a normal heat engine that extracts Q1 from warm body, transfers Q2 to cold body and does work Q=Q1-Q2
equivalence - the net result is
extraction of heat Q1-Q2 from the warm body
no change to cold body
work done W=Q1-Q2
If Clausius’s statement violates it is possible to
construct a machine which extracts heat from the warm body and converts this into work, without any other effect (in particular heat loss to the colder body)
this violates KP
equivalence
now consider a heat engine that violates KP - extracting Q1 from hot body at T1 to perform work W=Q1. Let this
run in parallel with normal heat engine (operating in reverse) that extracts Q2 from cold body and transfers Q3 to hot body
equivalence - energy conservation gives Q3=Q2+W = Q2+Q1 so
net result is a transfer of heat from bold body to warm body
violates Clausius
a heat engine works by a
heat injection from warm reservoir and a heat rejection to cold reservoir
carnot’s theorem can be used to derive
a stronger restriction on the efficiency based on the formulations of the second law
carnot’s theorem
no engine operating between two thermal reservoirs can be more efficient than a reversible engine operating between those reservoirs
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