Gases and Vapors

Abstract

Gases and vapors are naturally associated with foods and food processing systems. The equilibrium between food and water vapor determines temperatures achieved during processing. Dissolved gases in foods such as oxygen affect shelf life. Gases are used to flush packages to eliminate oxygen and prolong shelf life. Modified atmospheres in packages have been used to prolong shelf life of packaged foods. Air is used for dehydration. Gases are used as propellants in aerosol cans and as refrigerants. The distinction between gases and vapors is very loose because theoretically all vapors are gases. The term “vapor” is generally used for the gaseous phase of a substance that exists as a liquid or a solid at ambient conditions.

Problems

• 3.1. Air used for dehydration is heated by burning natural gas and mixing the combustion products directly with air. The gas has a heating value of 1050 BTU/ft³ at 70°F and 1 atm pressure. Assume the gas is 98% methane and 2% nitrogen.

  • (a) Calculate the quantity of natural gas in ft³ at 70 EF and 1 atm needed to supply the heating requirements for a dryer that uses 1500 lb dry air per hour at 170°F and 1 atm. Assume the products of combustion will have the same specific heat as dry air of 0.24 BTU/(lb. °F).

  • (b) If the air used to mix with the combustion gases is completely dry, what will be the humidity of the air mixture entering the dryer?

• 3.2. A package having a void volume of 1500 cm³ is to be flushed with nitrogen to displace oxygen prior to sealing. The process used involved drawing a vacuum of 700 mm Hg on the package, breaking the vacuum with nitrogen gas, and drawing another 700 mm Hg vacuum before sealing. The solids in the package prevent total collapse of the package as the vacuum is drawn; therefore, the volume of gases in the package may be assumed to remain constant during the process. If the temperature is maintained constant at 25 °C during the process, calculate the number of gmoles of oxygen left in the package at the completion of the process. Atmospheric pressure is 760 mm Hg.

• 3.3. Compression of air in a compressor is an adiabatic process. If air at 20°C and 1 atm pressure is compressed to 10 atm pressure, calculate:

  • (a) The temperature of the air leaving the compressor.

  • (b) The theoretical compressor horsepower required to compress 100 kg of air. The specific heat ratio of air is 1.40; the molecular weight is 29.

• 3.4. Air at 25 °C and 1 atm that contains water vapor at a partial pressure that is 50% of the vapor pressure at 25 °C (50% relative humidity) is required for a process. This air is generated by saturating room air by passing through water sprays, compressing this saturated air to a certain pressure, P, and cooling the compressed air to 25 °C. The partial pressure of water in the cooled saturated air that leaves the compressor is the vapor pressure of water at 25°C. This air is allowed to expand to 1 atm pressure isothermally. Calculate P such that after expansion, the air will have 50% relative humidity.

• 3.5. An experiment requires a gas mixture containing 20% CO₂, 0.5% O₂, and 79.5% N₂ at 1 atm and 20 °C. This gas mixture is purchased premixed and comes in a 10 L tank at a pressure of 130 atm gauge. The gas will be used to displace air from packages using a packaging machine that operates by drawing a vacuum completely inside a chamber where the packages are placed, displacing the vacuum with the gas mixture, and sealing the packages. The chamber can hold four packages at a time, and the total void volume chamber with the packages in place is 2500 cm³. How many packages can be treated in this manner before the pressure in the gas tank drops to 1 atm gauge?

• 3.6. A vacuum pump operates by compressing gases from a closed chamber to atmospheric pressure in order that these gases can be ejected to the atmosphere. A vacuum drier operating at 700 mm Hg vacuum (atmospheric pressure is 760 mm Hg) and 50°C generates 500 g of water vapor per minute by evaporation from a wet material in the dryer. In addition, the leakage rate for ambient air infiltrating the dryer is estimated to be 1 L/h at 1 atm and 20 °C.

  • (a) Calculate the total volume of gases that must be removed by the vacuum pump per minute.

  • (b) If the pump compresses the gas in an adiabatic process, calculate the theoretical horsepower required for the pump. The specific heat ratio for water is 1.30, and that for air is 1.40.

• 3.7. The mass rate of flow of air (G) used in correlation equations for heat transfer in a dryer is expressed in kg air/m²(h). Use the ideal gas equation to solve for G as a function of the velocity of flow (V, in m/h) of air at temperature T and 1 atm pressure.

• 3.8. Use van der Waals equation of state to calculate the work done on isothermal expansion of a gas from a volume of 10 to 300 m³ at 80°C. The initial pressure was 10 atm. Calculate the entropy change associated with the process.

• 3.9. A supercritical CO₂ extraction system is being operated at 30.6 MPa and 60 °C in the extraction chamber. The volume of CO₂ leaving the system measured at 101.3 kPa and 20 °C is 10 L/min. If the extraction chamber is a tube having a diameter of 50.6 mm and a length of 45 cm, calculate the residence time of the CO₂ in the extraction chamber. Residence time = volume of chamber/volumetric rate of flow in the chamber.