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Experimental Physics 2 - The Second Law of Thermodynamics 1
Experimental Physics EP2 Thermodynamics
– 2nd Law of Thermodynamics –Heat engines, Carnot cycle
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Experimental Physics 2 - The Second Law of Thermodynamics 2
Basis for 2nd law of thermodynamics
WUQ +D=The net heat added to system equals the change of the internal
energy of the system plus the work done by the system.21 QQ -=
Sadi Carnot1
P
V
2a
1121 WUUQ +-=
b
2212 WUUQ --=-
2121 WWQQ -=-
working substance
1
21
1 QQQ
QW -
=ºh
efficiency
Experimental Physics 2 - The Second Law of Thermodynamics 3
Wilhelm Ostwald
The 2nd law of thermodynamics
1
2
1
1QQ
QW
-=ºh?1-=h
perpetuum mobile of 2nd kind
Lord Kelvin: No cyclic process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work.
T1
T2
system
Q
W
Planck: It is impossible to construct a device, which is operating in a cycle, the sole result of which will be lifting up a weight due to a decrease of an internal energy of the heat bath.
Clausius: No process is possible whose sole result is the transfer of heat from a body of lower temperature to a body of higher temperature.
T1
T2
systemQ
All statements of the 2nd law of thermodynamics are equivalent.
Experimental Physics 2 - The Second Law of Thermodynamics 4
Equivalency of different statements
1
21
1 QQQ
QW -
=ºh
21 QQW -=
2Q
1Q=
1
P
V
21Q
2Q
T1
T2
T1
T2
system QW
'Q
Principle of Carathéodory:In an arbitrary neighborhood ofevery point in macroscopic statespace there are adjacent pointswhich cannot be reached fromthe first point by adiabaticmeans.
Experimental Physics 2 - The Second Law of Thermodynamics 5
Experimental Physics 2 - The Second Law of Thermodynamics 6
The Carnot cyclePressure
Volume
Isotherm expansion
Isotherm compression
Adiabatic expansion
Adiabatic compression
1
2
34
1T
2T
1Q
2Q
12 )1( QQ h-=
system
h
T1
T2
1Q W
system'h
2Q 2'Q
1'Q
21: QQWm -=
21 ''':' QQWm -=
0'0'' 1111 =-Þ=- QQmqqm
)'()'(' 2211 QQQQWW ---=-
'' 22 WWQQ -=-
Heat extracted from cooler is spent solely to produce work.
1)'( Qhh -=
Experimental Physics 2 - The Second Law of Thermodynamics 7
The Carnot cyclePressure
Volume
Isotherm expansion
Isotherm compression
Adiabatic expansion
Adiabatic compression
1
2
34
1T
2T
1Q
2Q
1
21QQ
-=h ÷÷ø
öççè
æ=== ò
1
21
2
111 ln
VVRTPdVWQ n ÷÷
ø
öççè
æ=
4
322 ln
VVRTQ n
const1 =-gTV
11
3221
--
=gg
VTVT11
1142
--
=gg
VTVT1
1
2
1
4
3
--
÷÷ø
öççè
æ=÷÷
ø
öççè
ægg
VV
VV
1
2Carnot 1
TT
-=h
1
2
1
2
TT
=
Experimental Physics 2 - The Second Law of Thermodynamics 8
Selected applications: U=U(V); CP - CVPressure
Volume
! = #$ % #% & ='$'& %
&( − &* %* − %(
+( = ,* − ,( +!(
%( %*
$(
$.
+(1
2
&(
&*
= ','% &
%* − %( + $ %* − %(
!+(
= ( − &*&(
','% &
= & '$'& %
− $
PTVP T
VPVUCC ÷
øö
çè涶
úû
ùêë
é+÷
øö
çè涶
=-
/$ − /% = & '$'& %
'%'& $
/$ − /% = &0*1%2%*
Experimental Physics 2 - The Second Law of Thermodynamics 9
Ø Adiabatic processes occur when there is no heat exchange.
Ø The efficiency of a heat engine is the ratio of the work done
to the total heat absorbed.
Ø According to the second law of thermodynamics it is
impossible for a heat engine working in a cycle to remove heat
from a reservoir and to convert it completely
into work without any other effects.
Ø The Carnot cycle consist of two isothermal
and two adiabatic processes.
Ø The efficiency of any Carnot engine depends
only on the temperature difference.
To remember!
Experimental Physics 2 - The Second Law of Thermodynamics 10
WATER