This document discusses the absolute thermodynamic temperature scale and the third law of thermodynamics. It shows that connecting heat engines in series results in the temperature of the last engine, Tn, not being able to reach absolute zero. This is because the heat rejected by each subsequent engine, Qn, cannot be zero according to the functional relationship between Qn-1/Qn and Tn-1/Tn, demonstrating that absolute zero cannot be reached on the Kelvin scale without violating the second law of thermodynamics.
1 of 2
Download to read offline
More Related Content
Lect 5
1. Absolute thermodynamic temp scale
= 1
2
1
For any heat engine. For a reversible cycle = 1, 2
So,
1
2
= 1, 2
T1
T2
Q1
Q2
Q2
Q3
T3
W1=Q1-Q2
W2=Q2-Q3
Q1
Q3
W3=Q1-Q3
1
2
= 1, 2 ;
2
3
= 2, 3
1
3
= 1, 3
, 1, 2 * 2, 3 = 1, 3
Hence the simplest function is :
1
2
=
1
2
From this functional relationship we can deduce absolute zero can not be reached. Lets us
connect n number of engines in series and let the last engine deliver some work while rejecting
heat to a sink at Tn. According to this relation
1
=
1
and hence ю, since
can not be zero. So absolute zero on a Kelvin scale can not be reached
Third law of thermodynamics.
Absolute zero on Kelvin scale
Can not be reached without violating
2nd law of thermodynamics
Engine
Engine
Engine
2. = 1
2
1
= 1
2
1
Efficiency of reversible heat engine
ref =
Q2
Q1 Q2
=
T2
T1 T2
HP =
Q1
Q1 Q2
=
T1
T1 T2
Internally reversible and externally irreversible process
TH
TL
QH
QL
Ta
Tb
Engine W
= ( )
= ( )
=
If and = then is max
But QH=0 and w=0
On the other hand if ,
0, 0, 0
So there is some optimal set of cycle temp for maximum
power output. Find optimum for max power.
Known are: , 駒, , ゐ , find max W
ch=100; cl=80; th=900; tl=300
qh=ch*(th-ta)
ql=cl*(tb-tl)
w=qh-ql
qh/ta=ql/tb
ta_theo=ch/(ch+cl)*th+cl/(ch+cl)*sqrt(th*tl)
tb_theo=cl/(ch+cl)*tl+ch/(ch+cl)*sqrt(th*tl)
Make a parametric table with Ta, Tb, Qh, QL, and w
Vary Ta from 900 to 630K and get the table solved.
Now you can see W as a function of Ta and Tb. Find
W_max from the table.