Modern Engineering Thermodynamics

Summary 139
The general open system energy rate balance:
_Q − _W +∑ _E mass
= ðd/dtÞ mu + mV 2 /2g c + mZg/g c
system
flow
Work modes of energy transport are not discussed in any course outside of thermodynamics and are very important
for utilizing the full capacity of the first law of thermodynamics. We need to understand and master the
work mode auxiliary equations, because they are often required in the solution of thermodynamic problems.
Some of the important work mode auxiliary equations are given in Table 4.10. The associated power equations
are given in Table 4.6 of the text.
The local equilibrium postulate allows us to deal with nonequilibrium states, and the state postulate defines the
number of independent thermodynamic properties required to determine the local equilibrium state (two, for a
simple system).
Heat transport of energy (heat transfer 1 Q 2 and heat transfer rate _Q ) is categorized into three modes: (1) conduction,
(2) convection, and (3) radiation. Heat transfer is sufficiently important to mechanical engineers that
most curricula have separate heat transfer courses. Consequently, the details of this subject are not emphasized
in a thermodynamics course. The heat transfer rate modes are summarized in Table 4.11.
Generally, if you are asked to determine a heat transfer in a problem statement, you should calculate it from the
first law energy balance rather than from one of the heat transfer mode auxiliary equations.
Table 4.10 Work Mode Auxiliary Equations
Work Mode
Equation
Moving boundary (general)
ð 1
W 2 Þ moving
= ∫ 2
1 pdV
boundary
Polytropic moving boundary (n ≠ 1)
ð 1
W 2 Þ polytropic ðn ≠ 1Þ
=
1 mR
− n ðT 2 − T 1 Þ
ideal gas
moving boundary
Rotating shaft
ð 1
W 2 Þ rotating
= ∫ 2
1 T! ⋅ d
shaft
Elastic ð 1
W 2 Þ elastic
= −∫ 2 1
Surface tension
ð 1
W 2 Þ surface
= −∫ 2 s dA
1
tension
Electrical current
ð 1
W 2 Þ electrical
= ∫ 2 1
current
Electrical polarization
ð 1
W 2 Þ electrical
= −∫ 2
1
polarization
!
Magnetic
H 2
ð 1
W 2 Þ magnetic
= − μ 0 Vð1 + χ m Þ
2 − H2 1
2
Chemical
ð 1
W 2 Þ chemical
= −∑ k
μ i ðm 2 − m 1 Þ i
μ i ¼ constant i = 1
Mechanochemical ð 1
W 2 Þ mechanochemical
= ∫ 2 1
Table 4.11 Heat Transfer Rate Modes
Heat Transfer Mode
Equation
Conduction
_Q cond
= − k t A dT
dx
Convection
_Q conv = hAðT ∞ − T s Þ