第四章理想气体的热力过程

TdscvdTpdvTdscpdTvdp
dscv dTRdv ds cp dT Rdp
Tv
Tp
scv
lnT2 T1
Rlnv2 v1
scplnTT12
Rlnp2 p1
scplnvv12
Rlnp2 p1
w pdv
wt vdp
q Tds
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4.1 Basic Thermodynamic Process
(3) Work Applying
dthoTenedfiarsnstdclHavdweaTtofTrtahnesrfmerordeydns(功am量ci和cvs热lnt量oTT)t12he
process
Replacing δW with the reversible work
dUQW
since the volume is constant dV = 0
dUQPdV
W0 QdU
q du
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using the definition of the specific heat at constant volume
to replace dU in the first law.
QmCVdT
Q
m
T2 T1
CV
dT
The technical work done
Tds pdv
ds pdv T
ds Rdv v
s R ln v2 v1
s R ln p1 p2
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(3)功量和热量
Work Done and Heat Transferred
In an isothermal process, the temperature is constant. Applying the first law of thermodynamics to this closed process
pvk C
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When the temperatures at the start and end of the process are known, the pressure is calculated from
p2
(T2
)
k k 1
p1 T1
T2 ( v1 )k 1 T1 v2
4.绝热过程 Adiabatic Process
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(1) Process equation (过程方程)
Quasi-static, adiabatic process for an ideal gas
δq = cvdT + pdv and δq = cpdT – vdp
(确定在一个过程中系统与外界所交换的功量和热量的多少)
2. 本章研究的对象 The object of this chapter Reversible processes of Ideal Gases in closed systems
(闭口系统中理想气体的可逆过程)
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T2
v1 v2 T1 T2
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(2)内能、焓及熵的变化量 The change in Internal Energy, Enthalpy
and Entropy
ducvdT qcvdTpdv
q dh
dhcpdT
qcvdT d(p)v
The amount of heat added to a closed system during a constant pressure process equals to the increase in enthalpy.
(2) The change in Internal Energy, Enthalpy
and Entropy (内能、焓及熵的变化量）
Entropy Change There is no heat transfer to or from the gas and the process is reversible so that
then cvdT = -pdv and cp dT =vdp

therefore cp v dp
then
cv p dv
or
klnv2 lnp2 0 or
finally, weva1rrive apt1the very
dv dp k usefupplv12evv1x2kk pre1spsion
from which it can also be shown that
p2
wt vdp 0
p1
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3. 等温压缩和膨胀
Isothermal Compression and Expansion
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(1)过程方程 (Process equation)
For a constant temperature process, the addition or removal of heat will lead to a change in the volume and pressure of the gas, as shown on the two graphs above.
5. 多变过程
Polytropic Process
Many processes can be approximated by the law:
Substitute
into
T C
p1v1 p2v2
T1
T2
p1v1p2v2
现在您浏览到是十六页，共四十六页。
(2) 内能、焓及熵的变化量
The change in Internal Energy, Enthalpy and Entropy
ducvdT0
dhcpdT0
qcvdTpdv
q pdv
qcdTpdv For an ideal gas, thve internal energy is a function of
temperature only, and since the temperature is constant, then dU is zero and
qwpdv
现在您浏览到是十八页，共四十六页。
using the ideal gas law and integrating between the start and end of the process
Q W mR V 2dT V mR ln V 2 TmR lnp T 1
V V 1
V 1
p2
During an isothermal process, the work done
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(3) Work Done and Heat Transferred(功量和热量)
When the temperatures at the start and end of the process are known, the work done is calculated from
addition or removal of heat will lead to a
change in the temperature and volume of the
gas, as shown on the two graphs above.
Substitute
into
pC
p1v1 p2v2
T1
w pdvcv(T2 T1)
2
2 pvk
1
w pdv
1
1
vk
dv
k
( 1
p1v1
p2v2
)
R(T1 T2) k 1
wt kw
Q 0
w t vdp
2
2
w t pdv d ( pv )
1
1
R (T1 T2 ) k 1
R (T2
T1)
k k 1 R (T1 T2 )
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(4.1 基本热力过程)
1. 等容过程 Isochoric-----Constant Volume process
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(1) 过程方程 (Process equation)
For a constant volume process, the addition or removal of heat will lead to a change in the temperature and pressure of the gas, as shown on the two graphs above.
现在您浏览到是十三页，共四十六页。
QdH
Q
m
T2 T1
CPdT
During a constant pressure process, heat is added or removed and the temperature and volume changes. The volume at the end of the process can be found using the ideal gas law and the work calculated from
A. It is to determine the change in the properties of working fluid
during a process; (在于确定在一个过程中工质状态参数的变化量)
B. It is to determine the amount of heat, work interaction between the system and its surroundings during a process.
by the system is equal to the heat added to the system, and all the work is technically usable.
wt p p1 2vdpp p1 2R pd Tp RlTnp p1 2
现在您浏览到是十九页，共四十六页。
现在您浏览到是十二页，共四十六页。
（3） Work done and Heat Transferred
qcvdTpdv
qcvdT d(p)v
q dh
The amount of heat added to a closed system during a constant pressure process equals to the increase in enthalpy.
Substitute
into
v C
p1v1 p2v2
T1
T2
p1 p2 T1 T2
现在您浏览到是六页，共四十六页。
(2)内能、焓及熵的变化量
The change in Internal Energy, Enthalpy and Entropy
qcvdTpdv
duqcvdT
dhcpdT
The amount of heat added to a closed system during a constant volume process equals to the increase in internal energy.
定容过程中加入闭口系统的热量等于系统的内能的增加量
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Entropy Change
To find the Entropy change, start with the expression derived from the first law, replacing dU using the definition of specific heat at constant volume and using the definition of entropy
内容总结
第四章理想气体的热力过程。气缸内的气体减少，气体状态不变化。(假设1-2和34的多变指数相等。Diagram.
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3. 所采取的步骤 The procedures adopted
Pv=RT
p1v1 p2v2
T1
T2
ucvT
hcpT
qcvdTpdv qcpdTvdp
p2
wt vdpv(p1p2)
p1
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2.等压过程 Isobaric-----Constant Pressure
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(1) 过程方程 Process equation
For a constant pressure process, the
确定在一个过程中系统与外界所交换的功量和热量的多少本章研究的对象theobjectchapterreversibleprocessesidealgasesclosedsystems闭口系统中理想气体的可逆过程1
第四章理想气体的热力过程
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1.本章的研究任务
The task of this chapter