热力学基础

Q=ΔE+A

系统从外界吸热时，Q为正<br>系统对外做功时，A为负<br>系统内能增加时，ΔE为正

等体过程&nbsp; &nbsp;<span class="equation-text" contenteditable="false" data-index="0" data-equation="Q_v=ΔE=\nu{i \over 2}RΔT"><span></span><span></span></span><br>等压过程&nbsp; &nbsp;<span class="equation-text" contenteditable="false" data-index="1" data-equation="Q_p="><span></span><span></span></span><span class="equation-text" contenteditable="false" data-index="2" data-equation="\nu{i+2 \over 2}RΔT"><span></span><span></span></span><br>等温过程&nbsp; &nbsp;<span class="equation-text" contenteditable="false" data-index="3" data-equation="Q_T=\nu RTln{V_2 \over V_1}"><span></span><span></span></span>

气体的摩尔定压热容&nbsp;&nbsp;<span class="equation-text" contenteditable="false" data-index="0" data-equation="C_{V，m}={i \over 2}R"><span></span><span></span></span>&nbsp;&nbsp;<br>气体的摩尔定压热容&nbsp;&nbsp;<span class="equation-text" contenteditable="false" data-index="1" data-equation="C_{p,m}=C_{V,m}+R={i+2 \over 2}R"><span></span><span></span></span>&nbsp;<br>比热比/泊松系数&nbsp;&nbsp;<span class="equation-text" contenteditable="false" data-index="2" data-equation="\gamma={C_{p,m} \over C_{V,m}}={i+2 \over i}"><span></span><span></span></span>

<span class="equation-text" contenteditable="false" data-index="0" data-equation="Q_V=\nu C_VΔT"><span></span><span></span></span>(不仅限于等体过程）<br><span class="equation-text" contenteditable="false" data-index="1" data-equation="Q_p=\nu C_pΔT"><span></span><span></span></span>

理想气体的绝热过程方程

<span class="equation-text" contenteditable="false" data-index="0" data-equation="A={p_1V_1-p_2V_2 \over \gamma-1}"><span></span><span></span></span>

多方过程

热机的效率&nbsp;&nbsp;<span class="equation-text" data-index="0" data-equation="\eta={A \over {Q_1}}={Q_1-Q_2 \over Q_1}=1-{ Q_2\over Q_1}" contenteditable="false"><span></span><span><br></span></span><span class="equation-text" data-index="1" data-equation="Q_1：吸收的热量 " contenteditable="false"><span></span><span></span></span>&nbsp; &nbsp; &nbsp;<span class="equation-text" data-index="2" data-equation="Q_2:放出的热量 " contenteditable="false"><span></span><span></span></span><br><span class="equation-text" data-index="3" data-equation="A：系统对外界所做的净功" contenteditable="false"><span></span><span></span></span><br><span style="font-size: inherit;">制冷机的效率/制冷系数&nbsp;<span class="equation-text" contenteditable="false" data-index="4" data-equation="\omega={Q_2 \over A}={Q_2 \over Q_1-Q_2}"><span></span><span></span></span></span><br>

卡诺循环是由两个等温过程和两个绝热过程组成的

卡诺循环的效率&nbsp; &nbsp;<span class="equation-text" contenteditable="false" data-index="0" data-equation="\eta_卡=1-{T_2 \over T_1}"><span></span><span></span></span>

开尔文表述：不可能从单一热源吸取热量，使之完全转化为有用的功而不产生其他影响。<br>克劳修斯表述：热量不可能自动地从低温物体传到高温物体。

卡诺定理：<br><span class="equation-text" data-index="0" data-equation="1. \eta=1-{T_2 \over T_1}" contenteditable="false"><span></span><span></span></span><br><span class="equation-text" contenteditable="false" data-index="1" data-equation="2. \eta_{不可逆}\leq\eta_{可逆}"><span></span><span></span></span><br>

<span class="equation-text" contenteditable="false" data-index="0" data-equation="S=k\ln W"><span></span><span></span></span><br>W 任一宏观状态所包含的微观状态数

热温比 dS=<span class="equation-text" contenteditable="false" data-index="0" data-equation="{dQ\over T}"><span></span><span></span></span>

熵的增量仅有初、末态决定<br>孤立系统的熵永不减少，即<span class="equation-text" contenteditable="false" data-index="0" data-equation="\triangle S\geq0"><span></span><span></span></span>