Ta where S  entropy dQ  differential of heat (very small change) Ta  absolute temperature The second law of thermodynamics can be expressed mathematically with the use of the entropy concept. Suppose an engine, which will convert heat into useful mechanical work, receives heat Q1 from a heat source at temperature T1 and delivers heat Q2 at a temperature T2 to a heat sink after performing work. By the first law of thermodynamics, the law of conservation of energy, Q2 is less than Q1 by the amount of work performed. And by the second law of thermodynamics, T2 is less than T1. The universe at the start of the process loses entropy S1  Q1 /T1 and at the end of the process gains entropy S2  Q2 /T2. Hence, the net change in the entropy of the universe because of this process will be S2
S1. Furthermore, this law requires that this net change must always be greater than zero and that the entropy increase is and must always be an irreversible thermodynamic process. Because of the irreversibility of the process, the energy that has become available for performing work is Q  T (S
S ) (13.7) u 2 2 1 13.2.5 Absolute Temperature The definition of entropy given above involves the concept of absolute temperature measured on a ratio scale. The unit of absolute temperature is measured in degrees Kelvin (
K) in the Celsius system and in degrees Rankine (
R) in the Fahrenheit system. Absolute zero or zero degrees in either system is determined by considering the theoretical behavior of an ideal gas, and for such a gas, P V  mRT or P v  RT (13.8) a a a a where Pa  absolute pressure on the gas, psf V  volume of the gas, ft3 v  specific volume of the gas, ft3 / lb  reciprocal of the gas density m  mass of the gas, lb Ta  absolute temperature R  universal gas constant For a gas under constant pressure, the absolute temperature theoretically will be zero when the volume is zero and all molecular motion ceases. Under these conditions, the absolute zero temperature has been determined to be nearly
273
C and
460
F. Therefore, Kelvin temperature
K  Celsius temperature  273
(13.9) Rankine temperature
R  Fahrenheit temperature  460
(13.10) In the Rankine system, the universal gas constant R equals 1545.3 divided by the molecular weight of the gas. For air, R  53.4, and for water vapor, R  85.8.

With carpet and pad 48 8-in concrete slab 35 With carpet and pad 57 21/2-in concrete on light metal forms, steel bar joists 27 With carpet and pad 50 TABLE 11.30 Performance of Commonly Used Sound Absorbents Absorbent Thickness, in. Density, lb per cu ft Noise reduction coefficient Mineral or glass fiber blankets 1/24 1/26 0.450.95 Molded or felted tiles, panels, and boards 1/211/8 825 0.450.90 Plasters (porous) 3/83/4 2030 0.250.40 Sprayed-on fibers and binders 3/811/8 1530 0.250.75 Foamed, open-cell plastics, elastomers, etc. 1/22 13 0.350.90 Carpets Varies with weave, texture, backing, pad, etc. Draperies Varies with weave, texture, weight, fullness Absorption coefficient per sq ft of floor area at frequencies. Hz: Seated audience 0.60 0.75 0.85 0.95 0.95 0.85 Unoccupied upholstered (fabric) seats 0.50 0.65 0.80 0.90 0.80 0.70 Acoustical Absorbents. Sound absorption coefficients and noise reduction coefficients of acoustical absorbents, including carpets and other furnishings, are usually readily available from manufacturers. The coefficients are normally obtained from laboratory tests of panel specimens of about 72- to 80-ft2 area, tested according to ASTM C423. It is imperative that the test specimens be as nearly identical as possible, in construction system and detail, with actual field installations, since construction details enormously affect acoustical performance. Table 11.30 lists performance ranges of typical absorbent materials. For specific data on specific materials or systems, always refer to specific tests by accredited

Propeller-type fans are also axial fans and are produced in many sizes and shapes. Small units are used for small jobs, such as kitchen exhausts, toilet exhausts, and air-cooled condensers. Larger units are used by industry for ventilation and heat removal in large industrial buildings. Such units have capacities of up to 200,000 ft3 /min of air. Propeller-type fans are limited to operating pressures of about 1/2 in water gage maximum, and are usually much noisier than centrifugal fans of equal capacities. Vaneaxial fans are available with capacities up to 175,000 ft3 /min and can operate at pressures up to 12 in water gage. Tubeaxial fans can operate against pressures of only 1 in water gage with only slightly lower capacities. In addition to the axial and centrifugal fan classifications, a third class for special designs exists. This classification covers tubular centrifugal fans and axialcentrifugal, power roof ventilators. The tubular centrifugal type is often used as a return-air fan in low-pressure HVAC systems. Air is discharged from the impeller in the same way as in standard centrifugal fans and then changed 90
in direction through straightening vanes. Tubular centrifugal fans are manufactured with capacities of more than 250,000 ft3 /min of air and may operate at pressures up to 12 in