Short Version : 18. Heat, Work, & First Law of Thermodynamics 短版:. 18

18.1. The 1st Law of Thermodynamics 熱力學第一定律 PE of falling weight 下墜重物的位能  KE of paddle 旋槳的動能  Heat in water 水中熱能 Either heating or stirring can raise T of the water. 加熱或攪拌都可以提升 T 。 1st Law of Thermodynamics 熱力學第一定律: Increase in internal energy = Heat added  Work done 內能增幅 = 所加熱量  所作功 Thermodynamic state variable = variable independent of history. 熱力態變數 = 跟歷程無關的變數 e.g., U, T, P, V, … Not Q, W, … Joule’s apparatus 焦耳的儀器

18.2. Thermodynamic Processes 熱力程序 Quasi-static process : Arbitrarily slow process such that system always stays arbitrarily close to thermodynamic equilibrium. 准靜態程序: 程序任意的慢，以使系統始終與熱力平衡隨意的近。 氣體 Reversible process: Any changes induced by the process in the universe (system + environment) can be removed by retracing its path. 可逆程序: 宇宙(系統+環境)因程序而引起的變化，都可由回溯其路徑而完全清除。 水 温度控制器 Twater = Tgas & rises slowly T水= T氣 & 緩慢上升 Reversible processes must be quasi-static. 可逆程序必為准靜態。 可動活塞 Irreversible process: Part or whole of process is not reversible. 不可逆程序: 部份或整個程序不是可逆的。 e.g., any processes involving friction, free expansion of gas …. 例: 任何涉及摩擦力的程序，氣體自由膨脹 …。 絕熱體 system always in thermodynamic equilibrium 系統始終維持在熱力平衡中 傳熱體

Work & Volume Changes 功&容積的變化 面積 Work done by gas on piston 氣體對活塞所作功

Isothermal Processes 等溫程序 Isothermal process : T = constant. 等(恆，定)溫程序 : T = 常數 熱庫  Isothermal processes on ideal gas 理想氣體的等溫程序

Constant-Volume Processes & Specific Heat 定容程序 & 比熱 Constant-volume process ( isometric, isochoric, isovolumic ) : V = constant 定容程序 ( 等距，等積，等容) : V = 常數  CV = molar specific heat at constant volume = 定(恆)容摩爾比熱  isometric processes 等距(積)程序 for all processes 所有程序 Ideal gas: U = U(T) 理想氣體  Non-ideal gas : 非理想氣體 only for isometric processes 祗有定容程序

Isobaric Processes & Specific Heat 等壓程序 & 比熱 Isobaric Process : constant P 等壓程序 : P 固定 Isotherms 等温線 CP = molar specific heat at constant pressure =定 (恆)壓摩爾比熱 isobaric processes 等壓程序 Ideal gas, isobaric : 理想氣體，等壓 : Ideal gas 理想氣體 

Adiabatic Processes 絕熱程序 Adiabatic process: Q = constant 絕熱程序: Q = 常數 e.g., insulated system, quick changes like combustion, … 例： 隔熱系统，高速變化如燃燒，… adiabat, ideal gas 絕熱線，理想氣體 靜止的活塞 Tactics 18.1.  策略 Prob. 66 Adiabatic: larger p 絕熱: 較大 p 移動中的活塞 Prob. 62 等温線 cdf

TACTIC 18.1. Adiabatic Equation 絕熱方程 Ideal gas, any process: 理想氣體，任何程序： Adiabatic process: 絕熱程序：   

Example 18.3. Diesel Power 柴油機的功率 Fuel ignites in a diesel engine from the heat of compression (no spark plug needed). 柴油機內的燃料由壓縮熱點燃 (無需火星塞 ) 。 Compression is fast enough to be adiabatic. 這壓縮很快，足以視為絕熱。 If the ignite temperature is 500C, what compression ratio Vmax / Vmin is needed? 如果點燃温度是 500C ，需要的壓縮比 Vmax / Vmin 為何？ Air’s specific heat ratio is  = 1.4, & before the compression the air is at 20 C. 空氣的比熱比為  = 1.4，且壓縮前空氣在 20 C。 氣缸 活塞 連接桿 曲柄軸

Ideal Gas Processes 理想氣體程序 等温 定容 等壓 絕熱 等壓線 絕熱線 等温線 定義性特徵 第一定律 氣體所作功 其他關係

Cyclic Processes 循還程序 Cyclic Process : system returns to same thermodynamic state periodically. 循還程序 : 系统週期性地回到同一個熱力態。

Example 18.4. Finding the Work 找出所作之功 An ideal gas with  = 1.4 occupies 4.0 L at 300 K & 100 kPa pressure. 一個  = 1.4 的理想氣體在 300 K 和100 kPa 壓力下佔了 4.0 L 。 It’s compressed adiabatically to ¼ of original volume, 它在絕熱下被壓到原來體積的 ¼ ， then cooled at constant V back to 300 K, 然後在定V 下冷回 300 K ， & finally allowed to expand isothermally to its original V. 最後則讓它以等温脹回原來的 V 。 How much work is done on the gas? 有多少功作在氣體上？ AB (adiabatic): 絕熱 BC (isometric): 等容 CA (isothermal): 等温 work done by gas: 氣體所作功

18.3. Specific Heats of an Ideal Gas 理想氣體的比熱   Experimental values ( room T ): 實驗數據 (室温) For monatomic gases 單原子氣體 ,   5/3, e.g., He, Ne, Ar, …. For diatomic gases 双原子氣體,   7/5 = 1.4, CV = 5R/2, e.g., H2 , O2 , N2 , …. For tri-atomic gases 叁原子氣體,   1.3, CV = 3.4R, e.g., SO2 , NO2 , …. Degrees of freedom (DoF) = number of independent coordinates required to describe the system 自由度 (DoF) = 描述系統所需獨立變數的數目 Single atom 單原子 : DoF = 3 (transl) For low T ( vib modes not active ) 低温 (振動模式未啓動) : Rigid diatomic molecule 定形双原子分子: DoF = 5 (3 transl + 2 rot) Rigid triatomic molecule 定形叁原子分子: DoF = 6 (3 transl + 3 rot)

The Equipartition Theorem 均隔定理 Equipartition theorem ( kinetic energy version): For a system in thermodynamic equilibrium, each degree of freedom of a rigid molecule contributes ½ kT to its average energy. 均分定理 (動能版) ：在一個熱力平衡的系统中，一個定形分子的每一個自由度 都對它的平均能量供獻 ½ kT。 Equipartition theorem ( general version): For a system in thermodynamic equilibrium, each degree of freedom described by a quadratic term in the energy contributes ½ kT to its average energy. 均分定理 (通用版) ：在一個熱力平衡的系统中，每一個在能量中以二次項表達 的自由度，都對它的平均能量供獻 ½ kT。 DoF ( f ) CV CP  Monatomic 3 3/2 5/2 5/3 Diatomic 5 7/2 7/5 Triatomic 6 4 4/3

Example 18.5. Gas Mixture 氣體混合物 A gas mixture consists of 2.0 mol of oxygen (O2) & 1.0 mol of Argon (Ar). 一個氣體混合物包含 2.0 mol 的氧 (O2) 和 1.0 mol 的氬 (Ar) 。 Find the volume specific heat of the mixture. 找出混合物的定容比熱。

Quantum Effects 量子効應 Quantum effect: 量子効應: Each mechanism has a threshold energy. 每個機制都有一個能量門檻。 Etransl < Erot < Evib E平移 < E轉動 < E振動 Translation+rotation+vibration 定積比熱 平移+轉動+振動 Translation + rotation 平移 + 轉動 Translation 平移 温度 CV of H2 gas as function of T. H2 氣體的 CV 隨 T 的變化。 Below 20 K hydrogen is liquid, 20 K 以下氫是液體， above 3200 K it dissociates into individual atoms. 3200 K 以上它分解成個別原子。

Reprise 重奏 Insulated gas 絕緣氣體 Quasi-static process : Arbitrarily slow process such that system always stays arbitrarily close to thermodynamic equilibrium. 准靜態程序: 程序任意的慢，以使系統始終與熱力平衡隨意的近。 Reversible process: Any changes induced by the process in the universe(system+environment) can be removed by retracing its path. 可逆程序: 宇宙(系統+環境)因程序而引起的變化，都可由回溯其路徑而完全清除。 Dissipative work: Work done on system without changing its configuration, irreversible. 消耗功: 作用在系统上卻不改變其組態的功，不可逆。 Insulated gas 絕緣氣體 a c : Free expansion with no diss. work. 自由膨脹，無消耗功。 c b : Adiabatic. 絕熱。 a d : Adiabatic. 絕熱。 d b : Free expansion with no diss. work. a e : Adiabatic. 絕熱。 e b : Adiabatic dissipative work. 絕熱消耗功。 1st law: The net adiabatic work done in all 3 processes are equal (shaded areas are equal). 第一定律：以上三個程序內的淨絕熱功相等 (兩暗影範圍的面積相同) 。