Chapter 4, Gases and Vapors Video Solutions, Fundamentals of Food Process Engineering

Problem 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 $1050 \mathrm{BTU} / \mathrm{ft}^3$ at $70^{\circ} \mathrm{F}$ and $1 \mathrm{~atm}$ pressure. Assume the gas is $98 \%$ methane and $2 \%$ nitrogen.
(a) Calculate the quantity of natural gas in $\mathrm{ft}^3$ at $70 \mathrm{EF}$ and $1 \mathrm{~atm}$. needed to supply the heating requirements for a dryer that uses $1500 \mathrm{lb}$ dry air per hour at $170^{\circ} \mathrm{F}$ and $1 \mathrm{~atm}$. Assume the products of combustion will have the same specific heat as dry air, of $0.24 \mathrm{BTU} /\left(\mathrm{lb} \cong{ }^{\circ} \mathrm{F}\right)$.
(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.

Manik Pulyani

Numerade Educator

02:55

Problem 2

A package having a void volume of $1500 \mathrm{~cm}^3$ is to be flushed with nitrogen to displace oxygen prior to sealing. The process used involved drawing a vacuum of $700 \mathrm{~mm} \mathrm{Hg}$ on the package, breaking the vacuum with nitrogen gas, and drawing another $700 \mathrm{~mm} \mathrm{Hg}$ vacuum before sealing. The solids in the package prevents 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 $25^{\circ} \mathrm{C}$ during the process, calculate the number of gmoles of oxygen left in the package at the completion of the process. Atmospheric pressure is $760 \mathrm{~mm} \mathrm{Hg}$.

Ma Ednelyn Lim

Numerade Educator

10:15

Problem 3

Compression of air in a compressor is an adiabatic process. If air at $20^{\circ} \mathrm{C}$ and 1 atm pressure is compressed to $10 \mathrm{~atm}$ pressure, calculate:
(a) The temperature of the air leaving the compressor;
(b) The theoretical compressor horsepower required to compress $100 \mathrm{~kg}$ of air. The specific heat ratio of air is 1.40; the molecular weight is 29 .

Eduard Sanchez

Numerade Educator

05:03

Problem 4

Air at $25^{\circ} \mathrm{C}$ and 1 atm that contains water vapor at a partial pressure that is $50 \%$ of the vapor pressure at $25^{\circ} \mathrm{C}$ ( $50 \%$ 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, $\mathrm{P}$, and cooling the compressed air to $25^{\circ} \mathrm{C}$. The partial pressure of water in the cooled saturated air that leaves the compressor is the vapor pressure of water at $25^{\circ} \mathrm{C}$. This air is allowed to expand to $1 \mathrm{~atm}$ pressure isothermally. Calculate $\mathrm{P}$ such that after expansion, the air will have $50 \%$ relative humidity.

M Hassan Anwar

Numerade Educator

02:16

Problem 5

An experiment requires a gas mixture containing $20 \% \mathrm{CO}_2, 0.5 \% \mathrm{O}_2$, and $79.5 \% \mathrm{~N}_2$ at $1 \mathrm{~atm}$ and $20^{\circ} \mathrm{C}$. This gas mixture is purchased premixed and comes in a $10 \mathrm{~L}$ 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 $\mathrm{cm}^3$. How many packages can be treated in this manner before the pressure in the gas tank drops to $1 \mathrm{~atm}$ gauge.

Crystal Wang

Numerade Educator

06:35

Problem 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 $700 \mathrm{~mm}$ $\mathrm{Hg}$ vacuum (atmmospheric pressure is $760 \mathrm{~mm} \mathrm{Hg}$ ) and $50^{\circ} \mathrm{C}$ generates $500 \mathrm{~g}$ 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 $1 \mathrm{~L} / \mathrm{h}$ at $1 \mathrm{~atm}$ and $20^{\circ} \mathrm{C}$.
(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 .

Khoobchandra Agrawal

Numerade Educator

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Problem 7

The mass rate of flow of air (G) used in correlation equations for heat transfer in a dryer is expressed in $\mathrm{kg} \mathrm{air} / \mathrm{m}^2(\mathrm{~h})$. Use the ideal gas equation to solve for $\mathrm{G}$ as a function of the velocity of flow $(\mathrm{V}$, in $\mathrm{m} / \mathrm{h})$ of air at temperature $\mathrm{T}$ and $1 \mathrm{~atm}$ pressure.

Victor Salazar

Numerade Educator

02:34

Problem 8

Use van der Waal's equation of state to calculate the work done on isothermal expansion of a gas from a volume of 10 to $300 \mathrm{~m}^3$ at $80^{\circ} \mathrm{C}$. The initial pressure was $10 \mathrm{~atm}$. Calculate the entropy change associated with the process.

Jake Rempel

Numerade Educator

01:15

Problem 9

A supercritical $\mathrm{CO}_2$ extraction system is being operated at $30.6 \mathrm{Mpa}$ and $60^{\circ} \mathrm{C}$ in the extraction chamber. The volume of $\mathrm{CO}_2$ leaving the system measured at $101.3 \mathrm{kPa}$ and $20^{\circ} \mathrm{C}$ is $10 \mathrm{~L} / \mathrm{min}$. If the extraction chamber is a tube having a diameter of $50.6 \mathrm{~mm}$ and a length of $45 \mathrm{~cm}$., calculate the residence time of the $\mathrm{CO}_2$ in the extraction chamber. Residence time $=$ volume of chamber/volumetric rate of flow in the chamber.

Hast Aggarwal

Numerade Educator