Latent Heat

The Physics Hypertextbook™
© 1998-2008 by Glenn Elert -- A Work in Progress
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Discussion

discussion

Name the 6 major phase changes (including synonyms).

Heat absorbed or released as the result of a phase change is called latent heat. There is no temperature change during a phase change, thus there is no change in the kinetic energy of the particles in the material. The energy released comes from the potential energy stored in the bonds between the particles.

exothermic (warming processes)
- condensation
  - warmer in the shower
  - steam radiators
- freezing
  - orange growers use ice to stop oranges from freezing
- deposition
  - snowy days are warmer than clear days in the winter
endothermic (cooling processes)
- evaporation / boiling
  - sweat
  - alcohol is "cool"
- melting
  - melting ice in drinks
- sublimation
  - cooling with dry ice

Scattered thoughts …

Under extreme conditions of heat and exercise, an individual may sweat more than a liter of liquid per hour.
The interior of roasted meat can never reach temperatures higher than the boiling point of water until all the water is cooked out of it, at which point it would resemble shoe leather. The outside is quickly dried out, however, and can reach the temperature of the surrounding cooking medium.
Cocoa butter is unique among the fats in that it is very regular in composition; whereas most other fats are actually mixtures. This gives it a very definite point; unlike butter, which softens gradually. As it melts in your mouth, it absorbs latent heat. This makes chocolate bars taste "cool". Cocoa butter is remarkably uniform in composition and structure: only three fatty acids in the majority of its triglycerides, with the same one occupying the middle position. Pure cocoa butter is quite brittle up to about 93 °F (34 °C), at which point it melts quite quickly.

elements	T_m (°C)	T_b (°C)	L_f (kJ/kg)	L_v (kJ/kg)
Normal* Phase Change Quantities for Selected Materials
aluminum	660	2519	397	10,900
argon	−189	−186	29.5	161
bismuth	271	1564	54.0	723
bromine (Br₂)	−7	59	132	375
chlorine (Cl₂)	−102	−34	181	576
copper	1084	2562	209	4730
gold	1064	2856	63.7	1645
helium	n/a	−269	3.45	20.7
hydrogen (H₂)	−259	−253	59.5	445
iron	1538	2861	247	6090
krypton	-157	-153	16.3	108
lead	327	1749	23.0	866
lithium	181	1342	432	21,200
mercury	−39	357	11.4	295
neon	−249	−246	16.8	84.8
nickel	1455	2913	298	6430
nitrogen (N₂)	−210	−196	25.3	199
oxygen (O₂)	−219	−183	13.7	213
plutonium (ε)	640	3228	11.6	1370
silicon	1414	3265	1790	12,800
silver	962	2162	105	2390
sodium	98	883	113	4240
sulfur	115	445	53.6	1400
tin	231	2602	59.2	2490
titanium	1668	3287	296	8880
tungsten	3422	5555	285	4390
uranium	1135	4131	38.4	1750
zinc	420	907	112	1890

compounds	T_m (°C)	T_b (°C)	L_f (kJ/kg)	L_v (kJ/kg)
alcohol, ethyl	−130	78
alcohol, methyl	−97	64.7
ammonia	−77.7	−33.3
butane	−138.4	−0.5	80.2
carbon dioxide	n/a	n/a	571	205
ethane	−172	−89	95.1
freon 12, −30 °C	−158	−29.8		166.2
freon 12, 0 °C	−158	−29.8		152.8
freon 12, +30 °C	−158	−29.8		136.3
methane	−182	−164	58.4	112
propane	−188	−44.5	80.1
water, 0 °C	0	100	334	2501
water, 25 °C	0	100		2441
water, 100 °C	0	100		2258
wax, beeswax	62

foods	T_m (°C)	T_b (°C)	L_f (kJ/kg)	L_v (kJ/kg)
butter	32~35
lard	41
margarine, table	34~37
margarine, bakery	38~43
oil, cocoa butter	34
oil, coconut	24
oil, corn	−20? −15?
oil, olive	−6
oil, palm	~35~
oil, peanut	3
oil, soya	−16? −13?
shortening, vegetable	44~50
sugar, fructose	104
sugar, glucose	146
sugar, sucrose	186
* Melting and boiling points are the "normal" values under one standard atmosphere of pressure. Latent heats of fusion and vaporization are measured at the normal melting and boiling points respectively, except where indicated.

Summary

All phase changes …
- take place at a specific temperature.
- take place without a change in temperature. (There is no temperature change during a phase change.)
- involve changes in internal potential energy.
- release or absorb latent heat.
  - Endothermic phase changes absorb heat from the environment. (They are cooling processes.)
  - Exothermic phase changes release heat to the environment. (They are warming processes.)
The specific latent heat (L) of a material …
- is a measure of the heat energy (Q) per mass (m) released or absorbed during a phase change.
- is defined through the formula Q = mL.
- is often just called the "latent heat" of the material.
- uses the SI unit joule per kilogram [J/kg].
There are three basic types of latent heat each associated with a different pair of phases.

	solid-liquid	liquid-gas	solid-gas
latent heat of …	fusion	vaporization	sublimation
endothermic phase changes	melting, liquefaction*	boiling, evaporation, vaporization	sublimation
exothermic phase changes	crystallization, freezing, fusion, solidification	condensation, liquefaction*	deposition
temperature	melting point, freezing point	boiling point, dew point	sublimation point, frost point
* Use of the word liquefaction should be avoided since the starting phase is ambiguous.

Problems

practice

Write something.
- Answer it.

In order to extract the maximum flavor in the shortest amount of time, your local fast food purveyor has decided to brew its coffee at 90 °C and serve it quickly so that it has only cooled down to 85 °C. While this may be economically sensible, it is negligent and dangerous from a health and safety standpoint. Water (which is what coffee mostly is) at 85 °C is hot enough to cause third-degree burns (the worst kind) in two to seven seconds. You decide to add ice cubes to your coffee to cool it down to a more reasonable 55 °C so you will be able to drink it sooner. (Watery brew be damned. You need your caffeine fix immediately.) How many 23.5 g ice cubes at -18.5 °C should you add to your 355 ml cup of coffee to accomplish your thermal goal?
Solution …

This is a conservation of energy problem. The heat gained by the ice will be equal to the heat lost by the coffee.

+Q_ice = −Q_coffee

This mixing problem is more complicated than the ones in the previous section, however. The ice must first warm up to its melting point (a temperature change), then it has to melt (a phase change), and then the liquid has to warm up (another temperature change). The coffee has less to do. It just has to cool down.


Q_cold ice	+	Q_melting	+	Q_melted ice	=	−Q_coffee
[mcΔT]_cold ice	+	[mL]_melting	+	[mcΔT]_melted ice	=	[mcΔT]_coffee

The final mixture will end up at one temperature. (Watch the order of subtraction when dealing with temperature changes.)


	m_ice(2,090 J/kg·C°)(0 + 18.5 °C)
+	m_ice(334,000 J/kg)
+	m_ice(4,200 J/kg·C°)(55 − 0 °C)	=	(0.355 kg)(4,200 J/kg·C°)(85 − 55 °C)
	m_ice(3603,665 J/kg)	=	(44,730 J)

	m_ice	=	0.0741 kg

This is about three ice cubes.

number = (74.1 g)/(23.5 g) ≈ 3 ice cubes

Write something different.
- Answer it.
Write something completely different.
- Answer it.

conceptual

The part of a refrigerator responsible for the actual cooling is a closed system of pipes that runs both inside and outside the refrigerator. The substance in the pipes easily changes between the liquid and gaseous phases. Which phase change takes place inside the refrigerator and which take place outside?

Resources

boiling
- Ionic solutions don't look like that!
- Why do many foods have High Altitude Cooking Instructions? Marshall Brain, How Stuff Works
humor
- Third-Grade Scientists Successfully Vaporize Water, The Onion, 28 November 2001
melting
- Theory of Ice skating is all wet!
- Thermal Clothing (microencapsulated phase-change material), Spinoff Magazine, NASA
- On the Preparation of Suppositories, William G. Ewing, American Journal of Pharmacy, Vol. 43, 1871.

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