18 Heat Work First Law of Thermodynamics 1

18. Heat, Work, & First Law of Thermodynamics 熱，功，和熱力學第一定律 1. 2. 3. The 1 st Law of Thermodynamics Thermodynamic Processes Specific Heats of an Ideal Gas 熱力學第一定律 熱力學程序 理想氣體的比熱

A jet aircraft engine converts the energy of burning fuel into mechanical energy. 一具噴射機引擎把燃燒燃料所得的能量轉變成機械能。 How does energy conservation apply in this process? 如何把能量守恆用到這個程序？ E combustion = E mech + Q waste E燃燒 = E機械 + Q廢棄

18. 1. The 1 st 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 。 1 st 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

Example 18. 1. Thermal Pollution 熱污染 The reactor in a nuclear power plant supplied energy at the rate of 3. 0 GW, 一個核電廠的反應爐以 3. 0 GW 的功率供應能量， boiling water to produce steam that turns a turbine-generator. 其間先把水燒成蒸氣，再以之推動一部渦輪發電機。 The spent steam is then condensed through thermal contact with water taken from a river. 用完的蒸氣則與一條河的水經過熱接觸後凝結。 If the power plant produces electrical energy at the rate of 1. 0 GW, at what rate is heat transferred to the river? 如果這發電廠以 1. 0 GW 的功率供應電能，熱傳到河裏的功率是多少？ 1 st law 第一定律 From standpoint of power plant: 以核電廠的角度來看： ( loses heat to river ) 流失到河裏

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 水 温度控 制器 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。 Twater = Tgas & rises slowly Reversible processes must be quasi-static. 可逆程序必為准靜態。 T水= T氣 & 緩慢上升 可動 活塞 Irreversible process: system is not retraceable (out of equilibrium during part / all of the process). 不可逆程序: 系統不可以回溯 (在部份／整個程序裏，不在 熱力平衡中)。 絕熱體 system always in thermodynamic equilibrium 系統始終維持在熱力平衡中 傳熱體 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 …。

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

GOT IT 懂嗎 ? 18. 1. Two identical gas-cylinder systems are taken from the same initial state to the same final state, but by different processes. 兩個一樣的汽缸系統，從同一個初態，經由不同的程序，達到同一個終態。 Which are the same in both cases 下面那一項在兩者都一樣: (a) the work done on or by the gas, 氣體所作或被作的功， (b) the heat added or removed, or 加入或移除的熱，或 (c) the change in internal energy? 內能的變化？

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

Example 18. 2. Bubbles 氣泡 ! A scuba diver is 25 m down, where the pressure is 3. 5 atm ( 350 k. Pa ). 一個潛水員在 25 m 水深處，壓力為 3. 5 atm ( 350 k. Pa ) 。 The air she exhales forms bubbles 8. 0 mm in radius. 她呼出的空氣形成半徑為 8. 0 mm 的氣泡。 How much work does each bubble do as it arises to the surface, assuming the bubbles remain at 300 K. 每個氣泡升到水面時作功多少？ 假定氣泡保持在 300 K。 T = const

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 Ideal gas: U = U(T) 理想氣體 Non-ideal gas : 非理想氣體 等距(積)程序 for all processes 所有程序 only for isometric processes 祗有定容程序

Isobaric Processes & Specific Heat 等壓程序 & 比熱 Isobaric Process : constant P Isotherms 等温線 等壓程序 : P 固定 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，… 靜止的活塞 Tactics 18. 1. 策略 adiabat, ideal gas 絕熱線， 理想氣體 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：

Conceptual Example 18. 1. Ideal-Gas Law vs Adiabatic Equation 理想氣體定律對絕熱方程 The ideal gas law says p V = n R T, 理想氣體定律說 p V = n R T but the adiabatic equation says p V = const. 絕熱方程卻說 p V = const. Which is right ? 那一個對? Both are right. 都對。 The adiabatic equation is a special case where T V +1 絕熱方程是個在 T V +1 時的特例。

Making the Connection Suppose you halve the volume of an ideal gas with = 1. 4. What happens to the pressure if the process is (a) isothermal and (b) adiabatic? Ans: (a) p. V = const p = 2 p 0 (doubles) (b) p V = const p = p 0 2 = 2. 64 p 0

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

Application: Smog Alert! 應用: 煙霧警報！ Air is poor heat conductor convection is adiabatic. 空氣是不良熱導體 對流是絕熱程序。 If rising air cools slower than surrounding air, 如果上升空氣的冷卻比周邊的空氣慢， pollution rises high & can be dispersed. 汚染物就可以升很高而散掉。 Otherwise, smog. 反之，則成煙霧。

GOT IT 懂嗎 ? 18. 2. Name the basic thermodynamic process involved when each of the following is done to a piston-cylinder system containing ideal gas, 點出下列每項作用在一個理想氣體汽缸系統時，所牽涉的熱力程序， & tell also whether T, p, V, & U increase or decrease. 也說出 T, p, V, & U 是增加還是減少。 (a) the piston is lock in place & a flame is applied to the bottom of the cylinder, 活塞位置鎖定，汽缸底部以火燒之， (b) the cylinder is completely insulated & the piston is pushed downward, 汽缸完全隔熱，活塞往下推， (c) the piston is exposed to atmospheric pressure & is free to move, while the cylinder is cooled by placing it on a block of ice. 活塞外通大氣壓且可以自由移動，汽缸則放在一塊冰上冷卻。 (a) isometric 等容; T , p , (b) adiabatic 絕熱 ; T , p , V =const, U . V , U . (c) isobaric 等壓 ; T , p =const, V , U .

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 An ideal gas with = 1. 4 occupies 4. 0 L at 300 K & 100 k. Pa pressure. 一個 = 1. 4 的理想氣體在 300 K 和100 k. Pa 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 找出所作之功

18. 3. Specific Heats of an Ideal Gas 理想氣體的比熱 Ideal gas: 理想氣體 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 = 5 R/2, e. g. , H 2 , O 2 , N 2 , …. For tri-atomic gases 叁原子氣體, 1. 3, CV = 3. 4 R, e. g. , SO 2 , NO 2 , …. Degrees of freedom (Do. F) = number of independent coordinates required to describe the system 自由度 (Do. F) = 描述系統所需獨立變數的數目 Single atom 單原子 : Do. F = 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: Do. F = 5 (3 transl + 2 rot) Rigid triatomic molecule 定形叁原子分子: Do. F = 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 k. T 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 k. T。 Equipartition theorem ( general version): For a system in thermodynamic equilibrium, each degree of freedom described by a quadratic term in the energy contributes ½ k. T 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 k. T。 Do. F ( f ) CV CP Monatomic 3 3/2 5/3 Diatomic 5 5/2 7/5 Triatomic 6 3 4 4/3

Example 18. 5. Gas Mixture 氣體混合物 A gas mixture consists of 2. 0 mol of oxygen (O 2) & 1. 0 mol of Argon (Ar). 一個氣體混合物包含 2. 0 mol 的氧 (O 2) 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 H 2 gas as function of T. H 2 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 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. 自由膨脹，無消耗功。 a e : Adiabatic. e b : Adiabatic dissipative work. 絕熱。 絕熱消耗功。 1 st 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) 。