Specific Heat Capacity (比熱容)
Specific Heat Capacity of a substance is the quantity of heat required to raise the temperature of 1 kg of a
substance by 1℃.
物質的比熱容是指使 1 公斤物質的溫度升高 1℃所需要的熱量。
𝑄 = 𝑚𝑐 ∆𝑇
= 𝑃𝑡
The units for c are 𝐽 𝑘𝑔!" 𝐾 !"
c 的單位是𝐽 𝑘𝑔!" 𝐾 !"
Example 1
1. A block of metal of mass 1.5 kg which is suitably insulated is heated from 30 °C to 50 °C in 8 minutes
and 20 seconds by an electric heater coil rated 54 watts. Find;
用額定功率為 54 瓦的電加熱器線圈在 8 分 20 秒內將質量為 1.5 公斤並適當絕緣的金屬塊
從 30°C 加熱到 50°C。
a) The quantity of heat supplied by the heater：
加熱器提供的熱量：
𝑄 = 𝑃𝑡
= 54 × 500
= 27,000 𝐽
b) The heat capacity of the block：
金屬塊的熱容量：
𝑄 = 𝐶∆𝑇
27000 = 1.5𝑐 (50 − 30)
= 1,350𝐽𝐾 !"
c) Its specific heat capacity：
金屬塊的比熱容：
𝑐=
𝐶
𝑚
1350
1.5
= 900 𝐽 𝑘𝑔!" 𝐾 !"
=
Exercise
1. If 300g of paraffin is heated with an immersion heater rated 40 W, what is the temperature after 3 mins
if the initial temperature was 20℃? (Specific Heat Capacity for paraffin = 2,200 J 𝐾𝑔!" 𝐾 !" ).
如果用額定功率為 40W 的浸入式加熱器加熱 300g 石蠟，如果初始溫度為 20℃，3 分鐘後的
溫度是多少？（石蠟的比熱容 = 2,200 J Kg-1 K-1）。
2. A piece of copper of mass 60 g and specific heat capacity 390 J 𝐾𝑔!" 𝐾 !" cools from 90 °C to 40 °C.
Find the quantity of heat given out.
一塊質量為 60 g、比熱容為 390 J 𝐾𝑔!" 𝐾 !" 的銅從 90 °C 冷卻到 40 °C。找出發出的熱量。
3. A 50 W heating coil is immersed in a liquid contained in an insulated flask of negligible heat capacity.
If the mass of the liquid is 10 g and its temperature increases by 10 °C in 2 minutes, find the specific
heat capacity of the liquid.
將 50 W 加熱線圈浸入熱容可忽略不計的絕熱燒瓶中的液體中。如果液體的質量為 10 g，其溫
度在 2 分鐘內升高 10 °C，求液體的比熱容。
4. A metal cylinder mass 0.5 kg is heated electrically. If the voltmeter reads 15V, the ammeter 3A and the
temperatures of the block rises from 20 °C to 85 °C in ten minutes. Calculate the specific heat capacity
of the metal cylinder.
電加熱質量為 0.5 kg 的金屬圓柱體。 如果電壓表讀數為 15V，則電流表為 3A，塊的溫度在
十分鐘內從 20°C 上升到 85°C。 計算金屬圓柱體的比熱容。
Specific Latent Heat (比潛熱)
Specific Latent Heat of Fusion (熔解比潛熱)
A substance is the quantity of heat required to convert the unit mass of the substance from the solid to the
liquid state without change in temperature.
物質的熔解比潛熱就是質量為 1 kg 的固體，變為相同溫度的液體時，所需要的熱量。即
f＝
E
m
𝑚 is the mass of the substance, 𝐸 is the energy absorbed by the substance.
m 為物質的質量， E 為物質所吸收的能量。
The unit of
f
is J kg-1. The specific latent heat of vaporization of steam is 3.34 × 105 J kg-1.
 f 的單位為 J kg-1。蒸氣的汽化比潛熱的認可值為 3.34 × 105 J kg-1。
This means that every 1kg 0oC of ice needs 3.34 × 105 J of energy to change into 0oC water.
這表示每 1kg 的 0oC 的冰，變為 0oC 的水，需要 3.34 × 105 J 的能量。
Exercise
Specific Latent Heat of Fusion
Specific Heat Capacity of water
Specific Heat Capacity of Ice
(熔解比潛熱) = 3.34 × 105 Jkg-1；
(水的比熱容量) = 4200 Jkg-1oC-1；
(冰的比熱容量) = 2050 Jkg-1oC-1
1. (a) What is the energy absorbed by water with a mass of 0.2 kg to raise its temperature from 0 ℃ to
60 ℃? 質量為 0.2 kg 的水，溫度由 0oC 升至 60 oC，需要吸收的能量為多少？
(b) How much energy needs to be absorbed to melt ice of equal mass at 0 ℃ to into water at 0 ℃ to?
相等質量的 0oC 的冰，熔解成 60 oC 的水，需要吸收的能量為多少？
2. An ice maker can convert 0.1 kg of water from 20 ℃ to 0 ℃ ice in two minutes. On average, how
much energy does the ice maker remove from the water per second?
一部製冰機可在兩分鐘內把 0.1 kg 的水由 20 oC 轉變成為 0 oC 的冰。問製冰機平均每秒從水中
移去多少能量？
3. Wing uses a 400W heater to turn an ice cube with a mass of 0.05kg and a temperature of −10 ℃ into
water at a temperature of m 80 ℃. How long does it take?
詠兒利用 400W 發熱器把質量為 0.05kg、溫度為－10 oC 的冰塊變為溫度為 80 oC 的水。問需多
少時間？
Specific latent heat of vaporization (汽化比潛熱)
The specific latent heat of the vaporization of a substance is the heat required for a liquid with a mass
of 1 kg to become a gas of the same temperature.
物質的汽化比潛熱就是質量為 1 kg 的液體，變為相同溫度的氣體時，所需要的熱量。即
v＝ E
m
𝑚
is the mass of the substance, 𝐸 is the energy absorbed by the substance.
m 為物質的質量， E 為物質所吸收的能量。
The unit of
f
is J kg-1. The specific latent heat of vaporization of steam is 3.34 × 105 J kg-1.
 v 的單位為 J kg-1。蒸氣的汽比潛熱的認可值為 2.26 × 106 J kg-1。
This means that for every 1kg of water at 100 ℃ change to 100 ℃ vapor need, 2.26 × 106 J of energy.
這表示每 1kg 的 100oC 的水，變為 100oC 的水蒸氣，需要 2.26 × 106 J 的能量。
Exercise
Specific latent heat of vaporization of water (水的汽化比潛熱) = 2.26 x 106 J kg-1；
Specific heat capacity of water.
(水的比熱容量)
= 4 200 J kg-1oC-1。
1. Amy obtained the following data from the latent heat of the vaporization experiment:
倩儀從汽化潛熱實驗中得到下列的數據
Mass of vaporized water 汽化了水的質量 = 0.12 kg
Energy released by electric heater 電熱器釋放的能量 = 294 000 J
(a) Calculate the specific latent heat of vaporization of water.
計算水的汽化比潛熱。
(b) Compare with the stand value (2.26 × 106 J kg-1)
試與標準值(2.26 × 106 J kg-1)比較。
2. How much energy is needed to turn 0.3 kg of water at an initial temperature of 80oC into 100oC steam ?
要把 0.3 kg、初溫度為 25oC 的水變為 100oC 蒸氣，需全多少能量？
3. If an immersion heater heats a cup of water with a mass of 0.05 kg from 30oC to boiling point in 30
seconds. Ask
若一浸沒式加熱器在 30 秒內把杯質量為 0.05 kg 的水從 30oC 加熱至沸點。問
(a) What is the power of heater?
加熱器的功率?
(b) If the heater continues to vaporize all the water, how many minutes will it take?
若加熱器繼續把水全部水汽化，問需時多少分鐘？
Latent Heat (潛熱)
Target: Latent heat is the energy released or absorbed for an object to change phase (melt, boil,
freeze, etc.).
目標：物質變態時，所吸入或釋放潛藏的能量
𝐸 = 𝐸𝑛𝑒𝑟𝑔𝑦 (𝐽)
𝑃 = 𝑃𝑜𝑤𝑒𝑟 (𝑊)
𝑡 = 𝑇𝑖𝑚𝑒 (𝑠)
𝑚 = 𝑀𝑎𝑠𝑠 (𝑘𝑔)
𝑙 = 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑙𝑎𝑡𝑒𝑛𝑡 ℎ𝑒𝑎𝑡 (𝐽⁄𝑘𝑔)
𝐸 =𝑃∙𝑡
= 𝑀𝑙
melting / vaporization (溫度沒有變化)
Energy lost by a hot object = Energy absorbed by a cold object
熱物體失去的能量(有變態) = 冷物體所吸收的能量
m1 c1 ( T 高溫 – T 平均溫) + m1 l
熔解
/
汽化
= m2 c2 ( T 平均溫 – T 低溫)
P t = m c ( T 高溫 – T 低溫 ) + m l 熔解
/
汽化
水的汽化比潛熱 l v = 2260000 J / kg
水的熔解比潛熱 l f = 334000 J / kg
Exercise – Latent heat
1. 1. In an experiment to measure the specific latent heat of vaporization of water, the following results
were obtained: mass of vaporized water m = 0.53 kg, required energy E = 0.36 kWh
在量度水的汽化比潛熱的實驗中得出以下結果：已汽化水的質量 m = 0.53 kg，所需的能量 E =
0.36 kWh
(a) Find the specific latent heat of the vaporization of water.
求水的汽化比潛熱。
(b) Analyze the difference between the experimental value obtained in the following cases and the
standard value 2.26 x 10 6 J kg -1
試分析以下情況所得實驗值與標準值 2.26 x 10 6 J kg -1 有何差異。
(i)
If water vapor condenses on top of the heater and flows back into the cup.
若有水汽在電熱器頂部凝結後流回杯中。
(ii) If part of the boiling water splashes out of the cup.
若有部分沸水濺到杯外。
(iii) If any energy is lost to the surrounding environment.
若有能量散失到周圍的環境中。
2. Use an electric heater with an electric power of 200 W to heat 0.5 kg of water at 20 oC to vaporization.
使用一電功率為 200 W 的電熱器將 0.5 kg 20 oC 的水加熱至汽化。
(a)
If the heating time is 1 hour, how much water is left? Assuming no energy loss.
若加熱時間為 1 小時，求剩下的水還有多少？假設沒有能量流失。
(b)
How long will it take to completely vaporize all the water?
需時多久可將所有水完全汽化？
3. A cup of 0.5 kg coffee is 50℃ and put a 0.05 kg ice into coffee.
一杯 0.5 kg 咖啡的溫度為 50 oC。若加入一粒 0.05 kg 0 oC 的冰。
Let the specific heat capacity of coffee is 5000 J kg-1 oC-1
加入一粒 0.05 kg 0 oC 的冰。
(a) Find the mixing temperature of the coffee after the ice is completely melted.
求冰完全熔解混合後，咖啡的混合溫度？
(b) What is the minimum number of ice grains of the same size that should be added to bring the coffee
down to 0℃? (Hint: let n be the number of ice particles added,)
若要使咖啡降至 0 oC，至少要加入多少粒相同大小的冰？
(提示：設 n 為加入冰粒的數量，)
(c) If the ice has just been taken out from the -20℃ refrigerator and put into the coffee, try to find the
mixing temperature in part a) again?
Ice has a specific heat capacity of 2100 J/ kg oC
若冰剛從 - 20 oC 冰箱拿出來，便放入咖啡中，試再求 a)部的混合溫度？
冰的比熱容為 2100 J/ kg oC
4. Heat 0.1 kg of solid material with a 100 W electric heater. The figure is the temperature-time relationship
line diagram of the substance.
用一功率為 100 W 的電熱器加熱 0.1 kg 的固體物質。右圖為該物的溫度-時間關系線圖。
溫度/oC
100
50
0
100
200
300
時間/秒
(a) Find the (i) melting point, (ii) specific latent heat of fusion, and (iii) specific heat capacity 求該
固體的 (i) 熔點、(ii)熔解比潛熱和 (iii)比熱容？
(b) If a 50 W electric heater is used, try to plot the estimated heating curve on the graph.
若使用 50 W 的電熱器，試在圖中畫出估計的加熱曲線圖。