MOOC大学物理热力学第一定律(双语)
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摩尔定体热容
unit:J mol 1 K 1
The heat required to raise 1 mol of the gas by 10C at constant volume.
d QV CV dT d QV C V d T
f nCV T n RT 2
f CV R 2
Applying the first law of thermodynamics
Q 0
W 0 +
U + + +
Powk.baidu.comsible？
例：一理想气体系统由状态a沿acb到达状态b，有350J 热量传入系统，而系统作功 130J.
（1）经过adb过程，系统作功40J，传入系统的热量 Q＝ ？
T1 T2
T1 Q T2
Heat is energy that is transferred from one body to another because of a difference in temperature. 通过传热方式传递能量的量度，系统和外界之间存在 温差而发生的能量传递
2. Work done in volume changes (process variable)
p1 p2
p
1 ( p1 , V1 , T1 ) 2 ( p 2 ,V 2 , T2 )
V1 V2
o
V
21.1 Heat, Work and Internal Energy 1. Heat (process variable 过程量)
1 Calorie=4.186J mechanical equivalent of heat
dW Fdl pAdl pdV
W pdV
V1
V2
W>0, expansion , work done by the gas on the environment
系统对外界作正功
W<0, compression, work done Work equals area under the by the environment on the gas curve in a PV diagram. 外界对系统作正功 The work done in taking a system from one state to another depends not only on the initial and final states but also on the path or process.
热力学 准静态过程 摩尔热容 等温过程 等压过程 等容过程 绝热过程 单原子分子 双原子分子 多原子分子 自由度 能量均分原理 内能
Chapter 21 The first Law of Thermodynamics 21.1 Heat, Work and Internal Energy 21.2 The first Law of Thermodynamics 21.3 Applying the First Law of Thermodynamics
z
x
o
Three degrees of translational freedom
y
1 1 1 3 2 2 2 K m vx m vy m vz kT 2 2 2 2
(b) Diatomic molecules-contain two atoms, as O2
The center of mass of the molecule can translate in the x, y, and z directions. In addition, the molecule can rotate about three mutually perpendicular axes.
U Q W
W 0, Work by system W 0, Work on system
Q 0, Heat added Q 0, Heat lost
U U 2 U 1 T , U 0,
the change in internal energy( 内能的增量） T , U 0,
Three degrees of translational freedom 确定质心位置 Two degrees of rotational freedom 确定转轴位置 f=t+r＝3+2=5
Kt 1 1 1 2 2 2 m v Cx m v Cy m v Cz 2 2 2
1 2 1 2 K r I y I z 2 2
3. The internal energy of ideal gas U
Internal energy U: the sum of all the energy of all the molecules in an object. •Energy within molecules Kinetic energy of atoms
The principle of equipartition of energy : energy is shared equally among the active degrees of freedom, and in particular each active degree of freedom of a 1 molecule has on the average an energy equal to kT
2. Isobaric Processes（等压过程） (1)Process equation (2) PV diagram
thermodynamics quasistatic process molar specific heat isothermal process isobaric process isochoric process adiabatic process monatomic molecules diatomic molecules polyatomic molecules degrees of freedom principle of equipartition of energy internal energy
Chapter 21 The first Law of Thermodynamics
System(系统)： Objects that we want to consider Environment(外界)；everything else in the universe 系统以外的物体 Categories of system Isolated system(孤立系统): 与外界没有任何相互作用的 系统既没能量交换，也没物质交换。是一个理想模型。 Closed system(封闭系统): 只有能量交换, 没有物质交换。 Open system(开放系统): 不但有能量交换, 而且还进行物 质交换。
(2) DF of ideal gas for the three kinds of molecules
刚性分子：不考虑分子间原子的振动，只考虑平动加转动 (a) monatomic molecules-contain only a single atom, as He (Helium) f =t＝ 3
Potential energy between atoms＝0 (ideal gas)
•Potential Energy between molecules =0 (ideal gas） Internal energy is all of a system’s kinetic energy of translation, rotation and vibration of molecules.
（2）当系统由状态b沿曲线ba返回状态a时，外界对系统作 功 60J，则系统吸收热量Q＝ ？
P
c a O
b d
V
21.3 Applying the First Law of Thermodynamics 1. Isochoric Processes(等体过程) (1)Process equation (Restriction)过程方程 P (2) PV diagram cons tan t T
2
分子任何一个自由度的平均能量都相等，均为
1 k T 2
Monatomic gas Diatomic gas Polyatomic gas
3 3 U N kT nRT 2 2 5 5 U N kT nRT 2 2
6 6 U N kT nRT 2 2
Internal energy
p2
p
2 ( p2 ,V , T2 ) 1
( p 1 , V , T1 )
p1
p
1 ( p1 , V , T1 ) 2
V
等体升压
等体降压
p1
p2 o
( p 2 ,V , T2 )
V
o
V
V
QV
U1
U2
QV
U1
U2
(3) W 0
f QV U n RT 2
(4) Cv
molar specific heat at constant volume
dU dQ dW
Differential form
⑴热力学第一定律就是能量转化与守恒定律，它 是自然界中的一个普遍规律。 ⑵系统状态变化过程中，功与热之间的转换不 可能是直接的，总是通过物质系统来完成。向 系统传递热量，使系统内能增加，再由系统内 能减少来对外作功；或者外界对系统作功，使 系统内能增加，再由内能减少，系统向外界传 递能量： internal energy work heat
(c) Polyatomic molecules-contain three atoms
f=t+r＝3+3=3＋2＋1＝6 3 (平动自由度) 确定质心位置 2 (转动自由度) 确定转轴位置 1 (转动自由度) 确定转角
(3) The principle of equipartition of energy
f U n RT 2 f U n R T 2
f U RT 2
21.2 The first Law of Thermodynamics The change in internal energy of a closed system will be equal to the heat added to the system minus the work done by the system.
f f U nRT N kT 2 2
internal energy of one mol of an idea gas internal energy of n mol of an idea gas the change in internal energy
The internal energy is a state function of T. It depends only on the initial and final states and does not depend at all on how the system gets from one to the other.
(1) Degrees of Freedom (DF) DF: The number of independent ways molecules can possess (store) energy 自由度：决定某物体空间位置所用的独立坐标数
f t r v
t: translational motion r: rotational motion v: vibration
Quasistatic (准静态) process: a process in which every step goes slowly that it is never far away from an equilibrium state. And it can be represented by a smooth curve on the pressure-volume diagram. (PV 图) 砂子 活塞 气体
unit:J mol 1 K 1
The heat required to raise 1 mol of the gas by 10C at constant volume.
d QV CV dT d QV C V d T
f nCV T n RT 2
f CV R 2
Applying the first law of thermodynamics
Q 0
W 0 +
U + + +
Powk.baidu.comsible？
例：一理想气体系统由状态a沿acb到达状态b，有350J 热量传入系统，而系统作功 130J.
（1）经过adb过程，系统作功40J，传入系统的热量 Q＝ ？
T1 T2
T1 Q T2
Heat is energy that is transferred from one body to another because of a difference in temperature. 通过传热方式传递能量的量度，系统和外界之间存在 温差而发生的能量传递
2. Work done in volume changes (process variable)
p1 p2
p
1 ( p1 , V1 , T1 ) 2 ( p 2 ,V 2 , T2 )
V1 V2
o
V
21.1 Heat, Work and Internal Energy 1. Heat (process variable 过程量)
1 Calorie=4.186J mechanical equivalent of heat
dW Fdl pAdl pdV
W pdV
V1
V2
W>0, expansion , work done by the gas on the environment
系统对外界作正功
W<0, compression, work done Work equals area under the by the environment on the gas curve in a PV diagram. 外界对系统作正功 The work done in taking a system from one state to another depends not only on the initial and final states but also on the path or process.
热力学 准静态过程 摩尔热容 等温过程 等压过程 等容过程 绝热过程 单原子分子 双原子分子 多原子分子 自由度 能量均分原理 内能
Chapter 21 The first Law of Thermodynamics 21.1 Heat, Work and Internal Energy 21.2 The first Law of Thermodynamics 21.3 Applying the First Law of Thermodynamics
z
x
o
Three degrees of translational freedom
y
1 1 1 3 2 2 2 K m vx m vy m vz kT 2 2 2 2
(b) Diatomic molecules-contain two atoms, as O2
The center of mass of the molecule can translate in the x, y, and z directions. In addition, the molecule can rotate about three mutually perpendicular axes.
U Q W
W 0, Work by system W 0, Work on system
Q 0, Heat added Q 0, Heat lost
U U 2 U 1 T , U 0,
the change in internal energy( 内能的增量） T , U 0,
Three degrees of translational freedom 确定质心位置 Two degrees of rotational freedom 确定转轴位置 f=t+r＝3+2=5
Kt 1 1 1 2 2 2 m v Cx m v Cy m v Cz 2 2 2
1 2 1 2 K r I y I z 2 2
3. The internal energy of ideal gas U
Internal energy U: the sum of all the energy of all the molecules in an object. •Energy within molecules Kinetic energy of atoms
The principle of equipartition of energy : energy is shared equally among the active degrees of freedom, and in particular each active degree of freedom of a 1 molecule has on the average an energy equal to kT
2. Isobaric Processes（等压过程） (1)Process equation (2) PV diagram
thermodynamics quasistatic process molar specific heat isothermal process isobaric process isochoric process adiabatic process monatomic molecules diatomic molecules polyatomic molecules degrees of freedom principle of equipartition of energy internal energy
Chapter 21 The first Law of Thermodynamics
System(系统)： Objects that we want to consider Environment(外界)；everything else in the universe 系统以外的物体 Categories of system Isolated system(孤立系统): 与外界没有任何相互作用的 系统既没能量交换，也没物质交换。是一个理想模型。 Closed system(封闭系统): 只有能量交换, 没有物质交换。 Open system(开放系统): 不但有能量交换, 而且还进行物 质交换。
(2) DF of ideal gas for the three kinds of molecules
刚性分子：不考虑分子间原子的振动，只考虑平动加转动 (a) monatomic molecules-contain only a single atom, as He (Helium) f =t＝ 3
Potential energy between atoms＝0 (ideal gas)
•Potential Energy between molecules =0 (ideal gas） Internal energy is all of a system’s kinetic energy of translation, rotation and vibration of molecules.
（2）当系统由状态b沿曲线ba返回状态a时，外界对系统作 功 60J，则系统吸收热量Q＝ ？
P
c a O
b d
V
21.3 Applying the First Law of Thermodynamics 1. Isochoric Processes(等体过程) (1)Process equation (Restriction)过程方程 P (2) PV diagram cons tan t T
2
分子任何一个自由度的平均能量都相等，均为
1 k T 2
Monatomic gas Diatomic gas Polyatomic gas
3 3 U N kT nRT 2 2 5 5 U N kT nRT 2 2
6 6 U N kT nRT 2 2
Internal energy
p2
p
2 ( p2 ,V , T2 ) 1
( p 1 , V , T1 )
p1
p
1 ( p1 , V , T1 ) 2
V
等体升压
等体降压
p1
p2 o
( p 2 ,V , T2 )
V
o
V
V
QV
U1
U2
QV
U1
U2
(3) W 0
f QV U n RT 2
(4) Cv
molar specific heat at constant volume
dU dQ dW
Differential form
⑴热力学第一定律就是能量转化与守恒定律，它 是自然界中的一个普遍规律。 ⑵系统状态变化过程中，功与热之间的转换不 可能是直接的，总是通过物质系统来完成。向 系统传递热量，使系统内能增加，再由系统内 能减少来对外作功；或者外界对系统作功，使 系统内能增加，再由内能减少，系统向外界传 递能量： internal energy work heat
(c) Polyatomic molecules-contain three atoms
f=t+r＝3+3=3＋2＋1＝6 3 (平动自由度) 确定质心位置 2 (转动自由度) 确定转轴位置 1 (转动自由度) 确定转角
(3) The principle of equipartition of energy
f U n RT 2 f U n R T 2
f U RT 2
21.2 The first Law of Thermodynamics The change in internal energy of a closed system will be equal to the heat added to the system minus the work done by the system.
f f U nRT N kT 2 2
internal energy of one mol of an idea gas internal energy of n mol of an idea gas the change in internal energy
The internal energy is a state function of T. It depends only on the initial and final states and does not depend at all on how the system gets from one to the other.
(1) Degrees of Freedom (DF) DF: The number of independent ways molecules can possess (store) energy 自由度：决定某物体空间位置所用的独立坐标数
f t r v
t: translational motion r: rotational motion v: vibration
Quasistatic (准静态) process: a process in which every step goes slowly that it is never far away from an equilibrium state. And it can be represented by a smooth curve on the pressure-volume diagram. (PV 图) 砂子 活塞 气体