Concept explainers
A rigid tank contains a mixture of 4 kg of He and 8 kg of O2 at 170 K and 7 MPa. Heat is now transferred to the tank, and the mixture temperature rises to 220 K. Treating the He as an ideal gas and the O2 as a nonideal gas, determine (a) the final pressure of the mixture and (b) the heat transfer.
(a)
The final pressure of the mixture.
Answer to Problem 96RP
The final pressure of the mixture is
Explanation of Solution
Write the expression to caculate the mole number of
Here, molar mass of
Write the expression to caculate the mole number of
Here, molar mass of
Write the expression to caculate the total number of moles
Write the expression to caculate the partial volume of helium
Here, universal gas constant is
Write the equation to calculate the reduced temperature and pressure at initial state.
Write the expression to caculate the partial volume of helium
Here, the compressibility factor is Z
Write the expression to calculate volume of the tank.
Write the expression to calculate partial pressure at final stage.
Write the equation to calculate the reduced temperature of argon gas after mixing.
Here, temperature at final stage is
Write the equation to calculate the reduced volume of argon gas.
Here, the mole number of oxygen gas
Write the equation to calculate the pressure of argon and nitrogen gases.
Write the expression to calculate the total final pressure.
Conclusion:
Substitute
Substitute
Substitute
Substitute
Refer Table A-1, “Molar mass, gas constant, and critical2point properties”, obtain the critical temperature and pressure of oxygen as follows.
Substitue
Substitue
Refer to Figure A-15, obtain the compressibility factor for argon gas by reading the reduced temperature and reduced pressure of
Substitute
Substitute
Substitute
Substitute
Substitute
Refer to Figure A-15, obtain the reduced pressure of argon gas by reading the values of reduced temperature and reduced volume of
Substitute 0.39 for
Substitute
Thus, the final pressure of the mixture is
(b)
The amount of heat transfer into the closed system.
Answer to Problem 96RP
The amount of heat transfer into the closed system is
Explanation of Solution
Write the expression to obtain the initial and final reduced pressure of
Write the equation to calculate the reduced temperature of nitrogen gas.
Here, mixture temperature is
Write the closed system energy balance relation.
Here, input energy is
Write the expression to obtain the initial and final reduced pressure of
Write formula for enthalpy departure factor
Here, the molar enthalpy at ideal gas state is
Rearrange the Equation (XVIII) to obtain
Refer Equation (XIX) express as two states of enthalpy difference (final – initial).
Write the expression to calculate partial pressure at inital stage.
Write the expression to calculate the total inital pressure.
Conclusion:
Substitute
Refer Figure A-29, “Generalized enthalpy departure chart”, obtain the value of
Substitute
Substitute
Substitute
Substitute
Thus, the amount of heat transfer into the closed system is
Want to see more full solutions like this?
Chapter 13 Solutions
THERMODYNAMICS CONNECT ACCESS CARD
- A pipe fitted with a closed valve connects two tanks. One tank contains a 5-kg mixture of62.5 percent CO2 and 37.5 percent O2 on a mole basis at 30°C and 125 kPa. The secondtank contains 10 kg of N2 at 15°C and 200 kPa. The valve in the pipe is opened and thegases are allowed to mix. During the mixing process 100 kJ of heat energy is supplied tothe combined tanks. The temperature of the mixture after mixing process is 39.4C. Drawthe schematic diagram of the system and all the data displayed on it. List all the appropriate assumption before analysing the problem. Use subscript ‘m’ to designate mixture. After mixing process, determine (a) the total volume of the mixture and (b) the final pressureof the mixture. Consult the appropriate property tables for the molar masses and gas constants of the constituent gases from the separate PDF file provided on the portal.arrow_forwardA mixture consisting of “4” kg O2, “15” kg N2 and “2” kg CO2. The mixturehas a pressure of 2 bar and temperature “24” ºC. Determine the following. (iv) Volume and density of the mixture(v) Partial pressure and partial volume of each gasarrow_forwardExplain the liquid-vapor equilibrium of pure substances: properties of the two-phase mixture.arrow_forward
- A mixture of gases contains 6 moles of O2, 2 moles of CO, and 3 moles of H2 at 40∘F and 200 psia. Determine: (a) the partial pressures of the individual components of the mixture (psia) (b) the volume of the mixture (ft3). (Universal gas constant = 1545 ft−lb/lb-R)arrow_forward2:A mixture consisting of “5” kg O2, “12” kg N2 and “4” kg CO2. The mixture has a pressure of 2 bar and temperature “20” ºC. Determine the following. Volume and density of the mixture Partial pressure and partial volume of each gasarrow_forwardAn insulated rigid tank is divided into two compartments by a partition. One compartment contains 8 kg of oxygen gas at 42 ∘C and 100 kPa, and the other compartment contains 4 kg of nitrogen gas at 20 ∘C and 180 kPa. The partition is then removed and the two gases are allowed to mix. Part A Determine the mixture temperature after equilibrium has been reached. Express your answer to four significant figures. Part B Determine the mixture pressure after equilibrium has been reached. Express your answer to five significant figures and include the appropriate units.arrow_forward
- A perfect gas mixture consists of 5.6 kmol N2 and 5.5 kmol CO2. What is the apparent gas constant of the mixture?arrow_forwardA mixture of gases is assembled by first filling an evacuated 0.39-m3 tank with neon until the pressure is 35 kPa. Oxygen is added next until the pressure increases to 105 kPa. Finally, nitrogen is added until the pressure increases to 140 kPa. During each step of the tank’s filling, the contents are maintained at 60°C. Determine the mass of each constituent in the resulting mixture. The mass of neon is kg. The mass of oxygen is kg. The mass of nitrogen is kg.arrow_forwardA mixture consisting of 4 kg O2, 10 kg N2 and 4 kg CO2. The mixture has a pressure of 2 bar and temperature 20 oC. Determine the following. (i) Mole fraction of each gas (ii) Molar mass of the mixture (iii) Gas constant of the mixture (iv) Volume and density of the mixture (v) Partial pressure and partial volume of each gasarrow_forward
- Instructions: Show your entire solution. Indicate which table from the steam tables you utilized in your solution. 5. A 4.12-kg steam-water mixture at 1.0 MP is contained in an inflexible tank. Heat is added until the pressure rises to 3.5 MPa and the temperature to 400°C. Determine the heat added in kJ.arrow_forward4. A container with a volume of 280 liters contains an ideal gas mixture at 40°C and 6.9 bar with a molar composition of 70% O₂ and 30% CH4. Assuming molecular weights of Moz= 32 kg/kmol and MCH4 = 16 kg/kmol, determine the mass of methane (in kg) that would have to be added and the mass of oxygen (in kg) that would have to be removed to obtain a final mixture molar composition of 30% O₂ and 70% CH4 at the same temperature and pressure.arrow_forwardA mixture of ideal gases consists of 3 kg of nitrogen and 5 kg of carbon dioxide at a pressure of 300 kPa and a temperature of 20oC. Find (a) the mole fraction of each constituent, (b) the equivalent molecular weight of the mixture, (c) the equivalent gas constant of the mixture, (d) the partial pressures and the partial volumes, (e) the volume and density of the mixture, and (f) the cp and cv of the mixture.If the mixture is heated at constant volume to 40oC, find the changes in internal energy, enthalpy and entropy of the mixture. Find the changes in internal energy, enthalpy and entropy of the mixture if the heating is done at constant pressure.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY