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

= 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=, Q={t{1}}^{t_{2}} 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

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