Chapter 2 energy, energy transfer, general energy analysis

本章介绍了能量、能量传递和一般能量分析的概念。主要讨论了能量的形式，包括总能量、动能、势能，以及能量关系。此外，还介绍了封闭系统能量、热传递、做功和热力学第一定律等概念。最后，介绍了能量转换效率的计算方法。

Forms of Energy

total energy

$E, e=\frac{E}{m}$

E con be assigned a value n of zeros $E=0$

macroscopic: Kinetic, potential

microscopic: internal energy

Kinetic energy (KE)

$K E=\frac{1}{2} m v^{2} ; \quad k e=\frac{1}{2} v^{2}$

Potential energy (PE)

$P E=m g z, \quad p e=g z$

能量关系

$\begin{aligned} & E=U+K E+P E=U+\frac{1}{2} m V^{2}+m g z \\ & e=u+k e+p e=u+\frac{1}{2} V^{2}+g z \end{aligned}$

Stationary system

$\Delta E=\Delta U$

flow rate 流

volume flow rate 体积流

$\begin{aligned} & \dot{V}= A_{c} \cdot V_{\text {avg }} \end{aligned}$

$A_c$ 横截面积
$V_{avg}$ 平均速率

mass flow rate 质量流

$\dot{m}=\rho \cdot \dot{v}$

energy flow rate 能量流

$\dot{E}=\dot{m} e$

封闭系统能量

The only two forms of energy interactions associated with a closed system are

heat transfer

work

热传递

Heat 热

form of energie that is transferred heat between 2 system by virtue of a temperature difference.

$q=\frac{Q}{m}, Q=\int_{t_{1}}^{t_{2}} \dot{Q} d t$

adiabatic process 绝热过程

$Q=0$

热的传递形式

Conduction 热传导
Convention 热对流
Radiation 热辐射

做功

功和功率

work $w=\frac{w}{m} \quad(k J / \mathrm{kg})$
power $p=\dot{w}=\frac{w}{\tau}$

formal sign convention 符号约定

heat transfer to a system and work dons by a system are pasitif

Path functions point functions 路径函数和点函数

Path functions = inexact different $\delta$
point functions: exact different $d$
$\begin{aligned}
& \int{1}^{2} d v=\Delta v \
& \int{1}^{2} \delta w=w_{12} \left(not \Delta w\right)
\end{aligned}$

work of other form 其他形式的功

Electrical Work

$W_{e}=\int u I d t$

Mechanical Work

$W{i m}=\int{2}^{1} F d s$

Shaft (转动) Work

$W_{S}=2\pi nT$

Spring Work 弹簧功

$W{\text {spring }}=\frac{1}{2} k\left(x{2}^{2}-x_{1}^{2}\right)$

热力学第一定律 first law

Energy Balance

$E{in} - E{out} =\Delta E$

Simple Compressible System

$\Delta E=\Delta U+\Delta K E+\Delta P E$
$\begin{aligned}
& \Delta U=m\left(u{2}-u{1}\right) \
& \Delta K E=\frac{1}{2} m\left(U{2}^{2}-V{1}^{2}\right) \
& \Delta P E=m g\left(z{2}-z{1}\right)
\end{aligned}$

Stationary system

$\triangle P E=\triangle K E=0$
$\Delta E=\Delta U$

mechanisms (机理)

Heat Transfer Q
Work Transfer W
Mass Flow

$\begin{aligned}
& \Leftrightarrow \Delta E{\text {system }}=Q+W+\Delta E{\text {mass }} \
& \Leftrightarrow d E\text { system }=\delta Q+\delta W+d E\text { mass } \
& \Leftrightarrow d E / d t=\dot{Q}+\dot{W}+\dot{E}_{\text {mass }}
\end{aligned}$