Reading Property Tables讀取性質表

What you'll be able to do本章學習成果

• Navigate saturation, superheated, and compressed-liquid tables.查閱飽和表、過熱蒸氣表與壓縮液體表。
• Interpolate linearly between table entries.在表格項目之間進行線性插値。
• Use quality for two-phase states and the ideal-gas tables for air.對兩相狀態使用乾度，對空氣使用理想氣體表。
• Look up the gas constant $R = R_u/M$ for common gases.查得常見氣體的氣體常數 $R = R_u/M$。

Key relations關鍵公式

Why tables?為何查表？

For most real substances, the relationships among properties are too complex for a single equation. Measured values are compiled into tables — the steam tables for water, separate tables for each refrigerant, and ideal-gas tables for air. Correct table reading is a core engineering skill.對於大多數實際物質，各性質間的關係難以單一方程式描述。因此量測值被編成表格——水的蒸汽表、各冷媒專用表、空氣的理想氣體表。正確查表是工程师的核心學能。

Anatomy of the tables表格結構詳解

A typical substance comes with several tables:一般物質有多種表格：

• Saturation tables — indexed by T and by p. List saturated-liquid (f) and saturated-vapor (g) properties plus vaporization change (fg). Use inside the dome.飽和表——分別以 T 與 p 為索引。列出飽和液 (f)、飽和蒸氣 (g) 與永魔變化量 (fg)。用於圓頂內部。
• Superheated-vapor tables — right of the dome, where T and p are independent. List $v, u, h, s$.過熱蒸氣表——圓頂右側，T 與 p 獨立。列出 $v, u, h, s$。
• Compressed-liquid tables — often approximated by $y(T,p) \approx y_f(T)$.壓縮液體表——常以 $y(T,p) \approx y_f(T)$ 近似。

Each table uses a reference state — only changes in $u$, $h$, $s$ matter.每個表以一個參考狀態為基準——只有 $u$、$h$、$s$ 的變化量才有意義。

Two-phase states: quality兩相狀態：乾度

In the two-phase region $T$ and $p$ are not independent, so you need the quality $x$. Any property is the lever-rule blend:在兩相區中，$T$ 與 $p$ 並非獨立，因此需要乾度 $x$。任何性質的桿桿法則展開：

(See Properties of Pure Substances for the full treatment.)(詳見純物質性質。)

Linear interpolation線性插値

When your state falls between two rows, estimate by linear interpolation:當狀態介於兩行之間時，以線性插値估算性質：

The same idea extends to double interpolation (both T and p).同樣思路可延伸至雙重插値（同時對 T 與 p）。

Interpolation trainer插値練習器

A real saturated-water excerpt. Slide the target temperature: bracketing rows highlight and interpolation is worked out. Try 55 °C.實際飽和水表節選。滑動目標溫度：對應行將被標示，插値過程展開。嘗試 55 °C。

Representative steam-table values, abridged for practice. Real tables have finer spacing and more columns.

Ideal-gas tables理想氣體表

For ideal gases, $u$ and $h$ depend on temperature only, so a table indexed by $T$ gives $u(T)$, $h(T)$, and the entropy function $s^\circ(T)$. A short air excerpt:對理想氣體，$u$ 與 $h$ 僅與溫度有關，以 $T$ 為索引的表即可給出 $u(T)$、$h(T)$ 與 $s^\circ(T)$。空氣節選：

Use $\Delta h = h(T_2) - h(T_1)$ directly. Entropy: $s_2 - s_1 = s^\circ_2 - s^\circ_1 - R\ln(p_2/p_1)$.直接使用 $\Delta h = h(T_2) - h(T_1)$。熵變化：$s_2 - s_1 = s^\circ_2 - s^\circ_1 - R\ln(p_2/p_1)$。

Gas constants氣體常數

Each gas has its own $R = R_u/M$, with $R_u = 8.314$ kJ/kmol·K:每一氣體各有其常數 $R = R_u/M$，$R_u = 8.314$ kJ/kmol·K：

Putting it together綜合應用