Boxmath.weebly.com



SPECIFIC GRAVITYSpecific gravity is the density of a substance divided by the density of water. The density of water is 62.4 lb/ft3. Divide the density of any substance by this number to get its specific gravity. Specific Gravity=Density62.4lb/ft3 Ex: Copper has a density of 556 lb/ft3. What is copper’s specific gravity? SG = density/62.4 lb/ft3SG = 556 lb/ft3 ÷ 62.4 lb/ft3SG = 8.91Ex: Gold has a specific gravity of 19.36. What is its density?SG = density/62.4 lb/ft319.36 = density/62.4 lb/ft3(multiply both sides by 62.4)19.36 × 62.4 lb/ft3 = density 1208.06 lb/ft3 = densitySPECIFIC VOLUMESpecific volume indicates the volume that each pound of a gas occupies. The measurement is based on only 1 pound of the gas. The units are in cubic feet per pound.Specific volume and density are inversely related. Specific Volume=1Density or Density= 1Specific VolumeEx: Aluminum has a density of 171 lb/ft3. What is its specific volume? SV = 1/Density SV = 1÷171 lbft3SV = 0.00585 ft3/lbEx. Dry air has a specific volume of 13.33 ft3/lb. What is its density? D = 1/SV D = 1÷13.33 ft3/lb D = 0.075 lb/ft3Practice: The density of tungsten is 1210 lb/ft3. What would be its specific volume? The specific volume of red brass is 0.001865 ft3/lb. What would be its density? Aluminum has a density of 171 lb/ft3. What would be its specific gravity?Marble has a specific gravity of 2.596. What would be its density?GAS LAWS: Boyle’s LawThe volume of gas (V) varies inversely with the absolute pressure (P), provided the temperature stays constant. P1V1=P2V2Ex: If the original pressure is 45 psia and the original volume is 32 in3, what would be the new pressure if the new volume is 37in3?45 psia × 32 in3 = P × 37in31440 psia*in3 = P × 37in3(divide both sides by 37in3)1440 psia* in337in3 = P 38.92 psia = PGAS LAWS: Charles’ LawAt a constant pressure, the volume of a gas varies directly as to the absolute temperature, and at a constant volume, the pressure of a gas varies directly with the absolute temperature.(As gas is heated, it will expand)V1T1=V2T2 and P1T1=P2T2*We must convert the temperature from ℉ to the Rankine scale by adding 460°R to each given temperature.*If pressure is given in psig (pounds per square inch guage), we must convert to psia (atmospheric pressure) by adding 14.696 to the amount given in psig.Ex: If 1990 ft3 of air is passed through a gas-fired furnace and heated from 72°F room temperature to 120℉, what is the volume of the air leaving the heating unit? T1=72+460=532°R; T2=120+460=580°RNow put the values into the formula. We have the initial temperature, the initial volume, and the final temperature.1990532=V580Cross-multiply to solve the proportion.532V=1990?582532V=1154200Divide both sides by 532V = 2169.55 ft3Ex: If a natural gas tank is holding 425000 ft3 of gas and is stored at 50℉ in the winter and the temperature rises to 70℉ in the spring, what would the new pressure be if the original pressure was 24 psig in the winter?T1=50+460=510°R; T2=70+460=530°RP1=24+14.696 = 38.696 psiaNow put the values into the formula. We have the initial temperature, the final temperature, and the initial pressure.38.696510=P530 Cross-multiply to solve the proportion.510P=38.696×530510P = 20508.88Divide both sides by 510P = 40.21 psia or 25.5 psig (after subtracting 14.696 from 40.21)GENERAL LAW OF PERFECT GASA combination of Boyle’s and Charles’ laws, this law includes temperature, pressure, AND volume.P1×V1T1=P2×V2T2Ex: A container holds 15 ft3 of gas and is being stored at 95℉ with a pressure of 60 psig. This container is connected by a pipe to one that will hold 25 ft3 of gas, for a total volume of 40 ft3 of gas, and the gas is allowed to equalize between the two containers. The temperature is lowered to 75℉. What is the pressure of the combined containers?P1=60 psig+14.696=74.696 psia V1=15 ft3 T1=95℉+460= 555°R V2=40 ft3T2=75℉+460=535°RNow put the values into the formula, and remember that the unknown value here is the final pressure.74.696×15555=P×40535 Simplify1120.44555=40P535 Cross multiply to solve555×40P=1120.44×535Simplify22200P = 599435.4Divide by 22200 P = 27.002 psia – 14.696 = 12.306 psigPracticeWhose law states that the volume of a gas varies inversely with the absolute pressure, as long as the temperature remains constant? At a constant pressure, how does a volume of gas vary with respect to the absolute temperature? Four pounds of gas occupy 10ft3. What would be its total volume, density, and specific gravity?If 2010 ft3 of air is passed through a gas-fired furnace and heated from 75°F room temperature to 115℉, what is the volume of the air leaving the heating unit? If the original pressure is 46 psia and the original volume is 33 in3, what would be the new pressure if the new volume is 39in3?If a natural gas tank is holding 375,000 ft3 of gas and is stored at 45℉ in the winter and the temperature rises to 75℉ in the spring, what would the new pressure be if the original pressure was 22 psig in the winter?A container holds 18 ft3 of gas and is being stored at 95℉ with a pressure of 70 psig. This container is connected by a pipe to one that will hold 32 ft3 of gas, for a total volume of 50 ft3 of gas, and the gas is allowed to equalize between the two containers. The temperature is lowered to 75℉. What is the pressure of the combined containers? ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download