Compression work is, therefore,
W ¼
p 2 V 2 À p 1 V 1
À k À 1
ð
Þ
¼
395:41 À 56:78 Â 4
À0:4
¼ À420:77kJ
Alternatively,
T 2 ¼ T 1 Â p 2 V 2 =p 1 V 1
ð
Þ¼475:58K
From Tables A-1 and A-2, we find
c V ¼ 20:80kJ=kmol À K. It follows
W ¼ 0:1 Â 20:80 Â 273:15 À 475:58
ð
Þ ¼ À 421kJ, which agrees with the
above.
(The minus sign indicates that work is done on the gas.)
3.10 Energy Analyses of Processes in Open Systems
The first law energy analysis in the above is applied to closed systems. Engineering
devices are often open systems with mass flow (most of the time with energy flow
[energy in transit] as well) into and out of the system. The first law equations,
Eqs. (22) and (22A), can be formulated for open systems. A concise derivation of
the first law equation (as well as the exergy equation) for open systems is given in
Chaps. 7 and 10, and more detailed treatment of such problems can be found in
most engineering thermodynamics books.
3.11 The Story of Heat
Up to this point, the question of useful work has not been addressed. This chapter
presented the first phase of the story of heat: our understanding of heat and work (in
general terms) as the matter stood in 1850, the year Joule published his definitive
paper on the MEH and Clausius formulated the first law by introducing the internal
energy incorporating the MEH. At this point of time, there were two contradictory
views of the conversion of heat (or heat) into work: Carnot’s principle, which
viewed work production to be resulting from the transfer of heat (see Chap. 4) and
the view of Rumford–Mayer–Joule, i.e., the MEH, which viewed work production
to result from the consumption of heat (this chapter, Eq. (24)) [5].
Historically, Carnot’s contribution preceded Mayer–Joule’s contribution. It
turned out that Carnot’s “heat” and Joule’s “heat” were not the same entity, i.e.,
different versions of heat. The next two chapters address the question of useful
56
3 The First Law: The Production of Heat …
W ¼
p 2 V 2 À p 1 V 1
À k À 1
ð
Þ
¼
395:41 À 56:78 Â 4
À0:4
¼ À420:77kJ
Alternatively,
T 2 ¼ T 1 Â p 2 V 2 =p 1 V 1
ð
Þ¼475:58K
From Tables A-1 and A-2, we find
c V ¼ 20:80kJ=kmol À K. It follows
W ¼ 0:1 Â 20:80 Â 273:15 À 475:58
ð
Þ ¼ À 421kJ, which agrees with the
above.
(The minus sign indicates that work is done on the gas.)
3.10 Energy Analyses of Processes in Open Systems
The first law energy analysis in the above is applied to closed systems. Engineering
devices are often open systems with mass flow (most of the time with energy flow
[energy in transit] as well) into and out of the system. The first law equations,
Eqs. (22) and (22A), can be formulated for open systems. A concise derivation of
the first law equation (as well as the exergy equation) for open systems is given in
Chaps. 7 and 10, and more detailed treatment of such problems can be found in
most engineering thermodynamics books.
3.11 The Story of Heat
Up to this point, the question of useful work has not been addressed. This chapter
presented the first phase of the story of heat: our understanding of heat and work (in
general terms) as the matter stood in 1850, the year Joule published his definitive
paper on the MEH and Clausius formulated the first law by introducing the internal
energy incorporating the MEH. At this point of time, there were two contradictory
views of the conversion of heat (or heat) into work: Carnot’s principle, which
viewed work production to be resulting from the transfer of heat (see Chap. 4) and
the view of Rumford–Mayer–Joule, i.e., the MEH, which viewed work production
to result from the consumption of heat (this chapter, Eq. (24)) [5].
Historically, Carnot’s contribution preceded Mayer–Joule’s contribution. It
turned out that Carnot’s “heat” and Joule’s “heat” were not the same entity, i.e.,
different versions of heat. The next two chapters address the question of useful
56
3 The First Law: The Production of Heat …