Thermodynamics — 考前速记

核心公式

$W = p\Delta V$

$\Delta U = q + W$

符号速查表

过程	$\Delta U$	$q$	$W$
等体 (isochoric)	$\Delta U = q$	$\Delta U$	0
等压 (isobaric)	$\Delta U = q - p\Delta V$	$\Delta U + p\Delta V$	$-p\Delta V$
等温 (isothermal) — 理想气体	0	$-W$	$W$
绝热 (adiabatic)	$W$	0	$\Delta U$
循环 (cyclic)	0	$-W$	$W$

考前 checklist

• 记住内能 = 分子随机动能 + 势能的总和
• 对理想气体，$U$ 只与 $T$ 有关
• $\Delta U = q + W$ 中 $W$ 是 work done on the system
• 气体膨胀（$\Delta V > 0$）：$W$ 为负
• 气体压缩（$\Delta V < 0$）：$W$ 为正
• $p$-$V$ 图面积 = 功的大小
• 循环过程 $\Delta U = 0$
• 等体过程 $W = 0$

关键句

Internal energy = sum of random distribution of kinetic and potential energies of molecules.

$\Delta U = q + W$: increase in internal energy = heating of system (to system) + work done on system.