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ISAT 413 - Module III: Building Energy Efficiency

Topic 1: Gas Mixtures, P-v-T Behavior

Introduction to Building Energy Efficiency

Gas Mixtures

P-v-T Behavior

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Introduction

“Energy use in buildings accounts for 35% of the total primary energy consumption in the United States and 42% of the total energy costs, and produces 35% of all U.S. carbon emissions. Utility bills are a substantial part of a family budget, so residential energy efficiency affects the kinds of housing people can afford as well as their comfort level. …. Energy savings can be achieved simultaneously with overall enhancement of indoor air quality, occupant comfort, and work productivity.…”

(Quoted from CRC Handbook of Energy efficiency, 1994)

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Building Energy Efficiency Standards

The NAECA (National Appliance Energy Conservation Act) minimum standard for the major types of equipment in the residential sector are:

Heat Pumps—A 10.0 minimum SEER for 1992 Room Air Conditioners—An 8.6 EER in 1990 Gas/Oil Furnaces—A 0.78 annual fuel utilization efficiency in 1992 Refrigerator—A standard of 691 kWh/year in 1993 Electric Water Heaters—A 0.88 Energy Factor in 1990 Natural Gas Water Heaters—A 0.54 Energy Factor in 1990

(From CRC Handbook of Energy Efficiency, 1994)

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EER (Energy Efficiency Ratio):

What is SEER (Seasonal Energy Efficiency Ratio)?

kW

hrBtuEER

in Input Power

/ in Output Power14~10

237188506271308710 ..EER.~.SEER Temperature and humidity control are two key components of space conditioning. The temperature of the atmospheric air in air-conditioning applications ranges from about -10 to 50oC, i.e., air and water-vapor behavior very like ideal gas.

Two Common Terms Used in the Domestic Heating and cooling

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CHPF (Combined Heating Performance Factor):

CCPF (Combined Cooling Performance Factor):

kWWWW

Btu/hrQQ~CHPF

whahuhp

sh

in

in wtk

84

kWWWW

Btu/hrQQ~CCPF

whahuhp

sc

in

in wtk

106

Another Two Common Terms Used in the Domestic Heating and cooling: (for integrated systems)

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Energy-Efficient Appliances

Vacuum panel insulation refrigerators

EPRI/e-tech heat pump (http://www.aers.com/heatpump.html)

Integrated water heater and condensing gas furnaces (http://oee.nrcan.gc.ca/publications/infosource/pub/home/Heating_With_Gas_Chapter3.cfm?attr=4)

Air-source variable-speed heat pump

Ground-source two-speed heat pump

Electronic ignition for gas ranges

Heat pump dryers

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A mixture of two or more gases of fixed chemical composition is called a nonreacting gas mixture. The composition of a gas mixture is described by specifying either the mole fraction or the mass fraction of each component, defined as

where

Gas Mixtures

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The apparent (or average) molar mass and gas constant of a mixture are expressed as

and

9© The McGraw-Hill Companies, Inc.,1998

Dalton’s Law of Additive Pressures for the Mixture of Two Ideal GasesDalton’s Law of Additive Pressures for the Mixture of Two Ideal Gases

,BAm PPP if it existed alone at the mixture temperature and volume.

P-v-T Behavior of Gas Mixtures

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Amagat’s Law of Additive Volumes for

the Mixture of Two Ideal Gases

Amagat’s Law of Additive Volumes for

the Mixture of Two Ideal Gases

,BAm VVV if it existed alone at

the mixture temperature and pressure.

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Dalton's law of additive pressures states that the pressure of a gas mixture is equal to the sum of the pressures each gas would exert if it existed alone at the mixture temperature and volume.

Amagat's law of additive volumes states that the volume of a gas mixture is equal to the sum of the volumes each gas would occupy if it existed alone at the mixture temperature and pressure.

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Dalton's and Amagat's laws hold exactly for ideal-gas mixtures, but only approximately for real-gas mixtures. They can be expressed as

Dalton's law:

Amagat's law:

k

i

mmim PTVV1

,

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Here Pi is called the component pressure and Vi is called the component volume. Also, the ratio Pi/Pm is called the pressure fraction and the ratio Vi/Vm is called the volume fraction of component i. For ideal gases, Pi and Vi can be related to yi by

The quantity yiPm is called the partial pressure and the quantity yiVm, is called the partial volume.

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Compressibility Factors: One Way of Predicting Real-Gas Mixture P-v-TCompressibility Factors: One Way of Predicting Real-Gas Mixture P-v-T

Zi is the compressibility of each real gas component in the mixture (refer to Figure A.12)

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The P-v-T behavior of real-gas mixtures can be predicted by using generalized compressibility charts. The compressibility factor of the mixture can be expressed in terms of the compressibility factors of the individual gases as

where Z is determined either at Tm and Vm, (Dalton's law) or at Tm and Pm (Amagat's law) for each individual gas.

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Another Way of Predicting the P-v-T Behavior of a Real-Gas MixtureAnother Way of Predicting the P-v-T Behavior of a Real-Gas Mixture

Treat a real-gas mixture as a pseudopure substance with critical properties P´cr and T´cr

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The P-v-T behavior of a gas mixture can also be predicted approximately by Kay's rule, which involves treating a gas mixture as a pure substance with pseudocritical properties determined from

and

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The evaluation of intensive properties of a gas mixture involves averaging in terms of mass or mole fractions (e.g. pressure, temperature, and density). The extensive properties of a gas mixture, in general, can be determined by summing the contributions of each component of the mixture (e.g. mass, volume, weight, energy, enthalpy, and entropy). :

k

i

k

i

k

i

iiiiim

k

i

k

i

k

i

iiiiim

k

i

k

i

k

i

iiiiim

sNsmSS

hNhmHH

uNumUU

1 1 1

1 1 1

1 1 1

(kJ/K)

(kJ)

(kJ)

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and

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Use of Partial Pressures for Entropy EvaluationUse of Partial Pressures for Entropy Evaluation

Partial pressures (not the mixture pressure) are used in the evaluation of entropy changes of ideal-gas mixtures