Air Conditioners

Houses were "air conditioned" long before electricity was commonly available. One means of energy storage for air conditioning was made possible by the large Heat of Fusion(see below) of water. One metric ton of water (1000 kg) can store 334 MJ of energy, so a "one ton'" air conditioner can remove 334 MJ/day, and a "one ton" heater can provide the same amount of energy. It may seem odd to talk about "energy storage" for a process like air conditioning that removesenergy from the air, until we realize that most power companies experience the biggest demand on hot days.

When ice melts it absorbs huge quantities of heat, even though the temperature stays constant at O °C (32 °F) during the melting process. That's why it was reasonable to cut ice from lakes and ponds in winter, and store it in "ice houses" for summer cooling.

The density of ice is 0.92 g/cm³, which we can round to 1 g/cm³ in order to estimate that one metric ton of ice is just over 1 m³! In fact, ice was originally transported from mountains to cities for use as a coolant, and the original definition of a "ton" of cooling capacity (heat flow) was the heat to melt one ton of ice every 24 hours. This is the heat flow one would expect in a 3,000-square-foot (280 m²) house in Boston in the summer. In other familiar units, it is 317 k BTUs or 93kWh. Now we define one ton of HVAC capacity = 12,000 BTU/hour.

A large building can be cooled for a day or a week by ice hauled in by horse-drawn carts and stored in a reasonably small building, like the icehouse at the longest operating service station on historic Route 66 in illinois, making it a "full service" station. See Ice Houses. About 5000 BTU/hr is recommended^[1] for a 100 to 150 square foot room, like a 12' x 12' dorm room. Air conditioners are often rated in "tons", which historically was the heat removed by 1 ton of ice every 24 hours. Nowadays, 1 ton is defined as 12,000 BTU/hr, and 1 BTU = 1.06 kJ. So the 5000 BTU/hr air conditioner is a 0.42 ton unit.

How long could the ice in the Amber ice house cool the 12 x 12' dorm room? Assuming it is about 2.5 m high, the ice house holds 7.3 m x 4.9 m x 2.5 m = 89 m³ of ice. Since ice has a density of 0.92 g/cm³, which we'll round to 1 g/cm³, so 1 m³ of ice is 1 m³x(10² cm/m)³x 1 g/cm³ = 10⁶ g = 10³ kg = 1 metric ton. The building holds 89 metric tons, enough to cool the room for 89 tons/0.42 tons/day = 210 days.

Figure \(\PageIndex{1}\) The icehouse at Ambler's Texaco Station ^[2]

Storing Heat or "Cold"

Ice is still used in large building or campus-wide air conditioning or chilled water systems^[3]. Air conditioning systems, especially in commercial buildings, are the most significant contributors to the peak electrical loads seen on hot summer days. In this application a relatively standard chiller is run at night to produce a pile of ice. Water is circulated through the pile during the day to produce chilled water that would normally be the daytime output of the chillers.

Heat of Fusion

When heat energy is supplied steadily to ice (or any solid), the temperature climbs steadily until the melting point is reached and the first signs of liquid formation become evident. Thereafter, even though we are still supplying heat energy to the system, the temperature remains constant as long as both liquid and solid are present. Only when the last vestiges of the solid have disappeared does the temperature start to climb again.

This macroscopic behavior demonstrates quite clearly that energy must be supplied to a solid in order to melt it. On a microscopic level melting involves separating molecules which attract each other. This requires an increase in the potential energy of the molecules.

The heat energy which a solid absorbs when it melts is called the enthalpy of fusion or heat of fusion and is usually quoted on a molar basis. (The word fusion means the same thing as “melting.”) When 1 mol of ice, for example, is melted, we find from experiment that 6.01 kJ are needed. The molar enthalpy of fusion of ice is thus +6.01 kJ mol^–1, and we can write

\[\ce{H2O (s) -> H2O (l)}\nonumber\]

(0°C) ΔH_M = 6.01 kJ mol^–1

Selected molar enthalpies of fusion are tabulated below. Solids like ice which have strong intermolecular forces have much higher values than those like CH₄ with weak ones.

Example \(\PageIndex{1}\): Ice and Air Conditioning

What mass of ice at 0°C removes the same amount of heat from a house as a one-ton air conditioner operates for 12 hours? 1 ton of HVAC capacity = 12,000 BTU/hour, and 1 btu = 1,055.05585 joules^[4] A small room air conditioner might be 6500 BTU/h or around 700 Watts.

Solution

\[\text{12,000} \dfrac{\text{BTU}}{\text{hour}} \times \text{12 hours} \times \text{1055} \dfrac{\text{J}}{\text{BTU}} = \text{1.52} \times \text{10}^8 \text{J or 1.52} \times \text{10}^5 \text{kJ}\nonumber\]

\[\dfrac{\text{1.52} \times \text{10}^5}{\text{6.01} \dfrac{kJ}{mol}} = \text{2.53} \times \text{10}^4 \text{mol}\nonumber\]

\[\text{2.53} \times \text{10}^4 \text{mol} \times \text{18} \dfrac{g}{mol} = \text{4.55} \times \text{10}^5 \text{g or 455 kg}\nonumber\]

This is only about half a cubic meter!

Heat of Vaporization

When a liquid is boiled, the variation of temperature with the heat energy supplied is similar to that found for melting. When heat is supplied at a steady rate to a liquid at atmospheric pressure, the temperature rises until the boiling point is attained. After this the temperature remains constant until the enthalpy of vaporization has been supplied. Once all the liquid has been converted to vapor, the temperature again rises. In the case of water the molar enthalpy of vaporization is 40.67 kJ mol^–1. In other words

\[\ce{H2O (l) -> H2O (g)}\nonumber\]
(100°C) ΔH_M = 40.67 kJ mol^–1

Table \(\PageIndex{1}\) Molar Enthalpies of Fusion and Vaporization of Selected Substances.

Substance	Formula	ΔH(fusion) / kJ mol^1	Melting Point / K	ΔH(vaporization) / kJ mol^-1	Boiling Point / K	(ΔHv/Tb) / JK^-1 mol^-1
Neon	Ne	0.33	24	1.80	27	67
Oxygen	O2	0.44	54	6.82	90.2	76
Methane	CH4	0.94	90.7	8.18	112	73
Ethane	C2H6	2.85	90.0	14.72	184	80
Chlorine	Cl2	6.40	172.2	20.41	239	85
Carbon tetrachloride	CCl4	2.67	250.0	30.00	350	86
Water*	H2O	6.00678 at 0°C, 101kPa 6.354 at 81.6 °C, 2.50 MPa	273.1	40.657 at 100 °C, 45.051 at 0 °C, 46.567 at -33 °C	373.1	109
n-Nonane	C9H20	19.3	353	40.5	491	82
Mercury	Hg	2.30	234	58.6	630	91
Sodium	Na	2.60	371	98	1158	85
Aluminum	Al	10.9	933	284	2600	109
Lead	Pb	4.77	601	178	2022	88

*http://www1.lsbu.ac.uk/water/data.html

Heat energy is absorbed when a liquid boils because molecules which are held together by mutual attraction in the liquid are jostled free of each other as the gas is formed. Such a separation requires energy. In general the energy needed differs from one liquid to another depending on the magnitude of the intermolecular forces. We can thus expect liquids with strong intermolecular forces to have larger enthalpies of vaporization. The list of enthalpies of vaporization given in the table bears this out.

Two other features of the table deserve mention. One is the fact that the enthalpy of vaporization of a substance is always higher than its enthalpy of fusion. When a solid melts, the molecules are not separated from each other to nearly the same extent as when a liquid boils. Second, there is a close correlation between the enthalpy of vaporization and the boiling point measured on the thermodynamic scale of temperature. Periodic trends in boiling point closely follow periodic trends in heat of vaporiation. If we divide the one by the other, we find that the result is often in the range of 75 to 90 J K^–1 mol^–1. To a first approximation therefore the enthalpy of vaporization of a liquid is proportional to the thermodynamic temperature at which the liquid boils. This interesting result is called Trouton’s rule. An equivalent rule does not hold for fusion. The energy required to melt a solid and the temperature at which this occurs depend on the structure of the crystal as well as on the magnitude of the intermolecular forces.

From ChemPRIME: 10.9: Enthalpy of Fusion and Enthalpy of Vaporization

References

1. ↑ http://www.energystar.gov/index.cfm?c=roomac.pr_properly_sized
2. ↑ http://en.Wikipedia.org/wiki/Ambler%27s_Texaco_Gas_Station
3. ↑ http://en.Wikipedia.org/wiki/Thermal_energy_storage
4. ↑ http://wiki.answers.com/Q/How_many_BTU_per_Hour_equals_1_Ton_of_Air_Conditioning

Contributors and Attributions

• Ed Vitz (Kutztown University), John W. Moore (UW-Madison), Justin Shorb (Hope College), Xavier Prat-Resina (University of Minnesota Rochester), Tim Wendorff, and Adam Hahn.