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rewona [7]
2 years ago
12

A tank with a volume of 40 cuft is filled with a carbon dioxide and air mixture. The pressure within the tank is 30 psia at 70oF

. It is known that 2 lb of carbon dioxide was placed in the tank. Assume that air is 80% nitrogen and 20% oxygen and use the ideal gas laws. Calculate ,

Engineering
1 answer:
aliya0001 [1]2 years ago
8 0

The correct responses are;

(i) Weight percent of nitrogen: <u>58.6%</u>

Weight percent of oxygen: <u>14.65%</u>

Weight percent of carbon dioxide: <u>29.59%</u>

(ii) Volume percent of nitrogen: <u>64.38%</u>

Weight percent of oxygen: <u>14.1%</u>

Weight percent of carbon dioxide: <u>21.53%</u>

(iii) Partial pressure of nitrogen: <u>19.314 psia</u>

Partial pressure of oxygen: <u>4.23 psia</u>

Partial pressure of carbon dioxide: <u>6.459 psia</u>

(iv) Partial pressure of nitrogen: <u>19.314 psia</u>

Partial pressure of oxygen: <u>4.23 psia</u>

Partial pressure of carbon dioxide: <u>6.459 psia</u>

(v) The average molecular weight is approximately <u>32.02 g/mole</u>

(vi) At 20 psia, 60 °F, the density is<u> 0.11275 lb/ft.³</u>

At 14.7 psia, 60 °F, the density is <u>0.0844 lb/ft.³</u>

At 14.7 psia, 32 °F, the density is <u>0.0892 lb/ft.³</u>

(vii) The specific gravity of the mixture <u>0.169</u>

Reasons:

The volume of the tank = 40 ft.³ = 1.132675 m³

Content of the tank = Carbon dioxide and air

The pressure inside the tank = 30 psia = 206843 Pa

The temperature of the tank = 70 °F ≈ 294.2611 K

Mass of carbon dioxide placed in the tank = 2 lb.

Percent of nitrogen in the tank = 80%

Percent of oxygen in the tank = 20%

(i) 2 lb ≈ 907.1847 g

Molar mass of carbon dioxide = 44.01 g/mol

Number of moles of carbon dioxide = \displaystyle \mathbf{ \frac{907.1847 \, g}{44.01 \, g/mol}} \approx 20.613 \, moles

Assuming the gas is an ideal gas, we have;

\displaystyle n = \mathbf{\frac{206843\times 1.132674}{8.314 \times 294.2611} }\approx 95.7588

The number of moles of nitrogen and oxygen = 95.7588 - 20.613 = 75.1458

Let <em>x</em> represent the mass of air in the mixture, we have;

\displaystyle \mathbf{ \frac{0.8 \cdot x}{28.014} +  \frac{0.2 \cdot x}{32}}= 75.1458

Solving gives;

x ≈ 2158.92 grams

Mass of the mixture = 2158.92 g + 907.1847 g ≈ 3066.1047 g

\displaystyle Weight \ percent \ of \ nitrogen= \frac{0.8 \times 2158.92}{3066.105} \times 100 \approx \underline{58.6 \%}

\displaystyle Weight \ percent \ of \ oxygen = \frac{0.8 \times 2158.92}{3066.105} \times 100 \approx  \underline{14.65\%}

\displaystyle Weight \ percent \ of \ carbon \ dioxide = \frac{907.184}{3066.105} \times 100 \approx  \underline{29.59\%}

ii.

\displaystyle Number  \ of \ moles \ nitrogen= \frac{0.8 \times 2158.92 \, g}{28.014 \, g/mol}  \approx 61.65\,  moles

\displaystyle Number  \ of \ moles \ oxygen= \frac{0.2 \times 2158.92 \, g}{32 \, g/mol}  \approx 13.5\, moles

Number of moles of carbon dioxide = 20.613 moles

Sum = 61.65 moles + 13.5 moles + 20.613 moles ≈ 95.763 moles

In an ideal gas, the volume is equal to the mole fraction

\displaystyle Volume \ percent \ of \ nitrogen= \frac{61.65}{95.763} \times 100 \approx  \underline{64.38 \%}

\displaystyle Volume \ percent \ of \ oxygen = \frac{13.5}{95.763} \times 100 \approx  \underline{14.1\%}

\displaystyle Volume \ percent \ of \ carbon \ dioxide = \frac{20.613 }{95.763} \times 100 \approx  \underline{21.53\%}

(iv) The partial pressure of a gas in a mixture, P_A = \mathbf{X_A \cdot P_{total}}

Partial pressure of nitrogen, P_{N_2} = 0.6438 × 30 psia ≈ <u>19.314 psia</u>

Partial pressure of oxygen, P_{O_2} = 0.141 × 30 psia ≈ <u>4.23 psia</u>

Partial pressure of carbon dioxide, P_{CO_2} = 0.2153 × 30 psia ≈ <u>6.459 psia</u>

(v) The average molecular weight is given as follows;

\displaystyle Average \ molecular \ weight = \frac{3066.105\, g}{95.7588 \, moles} =  32.02 \, g/mole

(vi) At 20 psia 70 °F, we have;

Converting to SI units, we have;

\displaystyle n = \frac{137895.1456\times 1.132674}{8.314 \times 294.2611} \approx 63.84

The number of moles, n ≈ 63.84 moles

The mass = 63.84 moles × 32.02 g/mol  ≈ 2044.16 grams ≈ 4.51 lb

\displaystyle Density = \frac{4.51\ lb}{40 \ ft.^3} \approx  \underline{0.11275\, lb/ft.^3}

When the pressure is 14.7 psia = 101352.93 Pa, and 60 °F

\displaystyle n = \frac{101352.9\times 1.132674}{8.314 \times 288.7056} \approx 42.8247

The mass = 47.8247 moles × 32.02 g/mol  ≈ 1531.35 grams = 3.376 lb.

\displaystyle Density = \frac{3.376 \ lb}{40 \ ft.^3} \approx \underline{ 0.0844\, lb/ft.^3}

When the pressure is 14.7 psia = 101352.93 and 32 °F

\displaystyle n = \frac{101352.9\times 1.132674}{8.314 \times 273.15} \approx 50.5482

The mass = 50.5482 moles × 32.02 g/mol  ≈ 1618.55 grams = 3.568 lb.

\displaystyle Density = \frac{3.568 \ lb}{40 \ ft.^3} \approx \underline{ 0.0892 \, lb/ft.^3}

(vii) \displaystyle The \ specific \ gravity \ of \  the  \ mixture \ = \frac{\frac{3066.1047\, g}{40 \, ft.^3} }{1.00} = \frac{\frac{6.7596 \, lbs}{40 \, ft.^3} }{1.00}   \approx  \underline{0.169}

Learn more about partial pressure here:

brainly.com/question/19813237

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ioda

Answer:

a) Qe = 0.01963 m^3 / s , mass flow rate m^ = 0.1334 kg/s

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Explanation:

Given:-

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                  Pressure ( Pe ) = 825 KPa

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Solution:-

- Define inlet parameters:

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                  Temperature = Ti = 20.0

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- From definition the volumetric flow rate at outlet ( Qe ) is determined by the following equation:

                   Qe = Ae*Ve

Where,

           Ae: The exit cross sectional area

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Therefore,

                  Qe = Ve*π*de^2 / 4

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                  Qe = 0.01963 m^3 / s

 

- To determine the mass flow rate ( m^ ) through the compressor we need to determine the density of air at exit using exit conditions.

- We will assume air to be an ideal gas. Thus using the ideal gas state equation we have:

                   Pe / ρe = R*Te  

Where,

           Te: The absolute temperature at exit

           ρe: The density of air at exit

           R: the specific gas constant for air = 0.287 KJ /kg.K

             

                ρe = Pe / (R*Te)

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- The mass flow rate ( m^ ) is given:

               m^ = ρe*Qe

                     = ( 6.79566 )*( 0.01963 )

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- We will use the "continuity equation " for steady state flow inside the compressor i.e mass flow rate remains constant:

              m^ = ρe*Ae*Ve = ρi*Ai*Vi

- Density of air at inlet using inlet conditions. Again, using the ideal gas state equation:

               Pi / ρi = R*Ti  

Where,

           Ti: The absolute temperature at inlet

           ρi: The density of air at inlet

           R: the specific gas constant for air = 0.287 KJ /kg.K

             

                ρi = Pi / (R*Ti)

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Using continuity expression:

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               Ai = 0.1334 / 1.18918*1

               Ai = 0.11217 m^2          

- From definition the volumetric flow rate at inlet ( Qi ) is determined by the following equation:

                   Qi = Ai*Vi

Where,

           Ai: The inlet cross sectional area

                  Qi = 0.11217*1

                  Qi = 0.11217 m^3 / s    

- The equations that will help us with required plots are:

Inlet cross section area ( Ai )

                Ai = m^ / ρi*Vi  

                Ai = 0.1334 / 1.18918*Vi

                Ai ( V ) = 0.11217 / Vi   .... Eq 1

Inlet flow rate ( Qi ):

                Qi = 0.11217 m^3 / s ... constant  Eq 2

               

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<em>Additional comment</em>

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Answer:

Explanation:

Note: In case of any queries, just comment in box I would be very happy to assist all your queries

SourceCode:

// MyGUI.java:

// Import packages

import java.awt.FlowLayout;

import java.awt.GridLayout;

import java.awt.event.ActionEvent;

import java.awt.event.ActionListener;

import java.io.BufferedReader;

import java.io.IOException;

import java.io.InputStreamReader;

import java.util.EmptyStackException;

import java.util.Stack;

import javax.swing.JButton;

import javax.swing.JFrame;

import javax.swing.JLabel;

import javax.swing.JOptionPane;

import javax.swing.JPanel;

import javax.swing.JTextField;

import javax.swing.SwingConstants;

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abstract class MyGUI extends JFrame implements ActionListener {

JTextField userInput;

JLabel inputDescLbl, resultLbl;

JPanel inputPanel, resultPanel;

JButton evlBtn;

Stack<Object> stk;

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super("Tree Address Generator");

inputPanel = new JPanel(new FlowLayout());

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userInput = new JTextField(20);

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evlBtn.addActionListener(this);

resultLbl = new JLabel("Infix Expression:", SwingConstants.LEFT);

add(inputPanel);

add(resultPanel);

inputPanel.add(inputDescLbl);

inputPanel.add(userInput);

inputPanel.add(evlBtn);

resultPanel.add(resultLbl);

stk = new Stack<Object>();

}

}

//Stack.java:

// Declare and define the class Stack

class Stack {

private int[] a;

private int top, m;

public Stack(int max) {

m = max;

a = new int[m];

top = -1; }

public void push(int key) {

a[++top] = key; }

public int pop() {

return (a[top--]); }

}

// Declare and define the class Evaluation()

class Evaluation {

public int calculate(String s) {

int n, r = 0;

n = s.length();

Stack a = new Stack(n);

for (int i = 0; i < n; i++) {

char ch = s.charAt(i);

if (ch >= '0' && ch <= '9')

a.push((int) (ch - '0'));

else if (ch == ' ')

continue;

else {

int x = a.pop();

int y = a.pop();

switch (ch) {

case '+':

r = x + y;

break;

case '-':

r = y - x;

break;

case '*':

r = x * y;

break;

case '/':

r = y / x;

break;

default:

r = 0;

}

a.push(r);

}

}

r = a.pop();

return (r);

}

}

// PostfixToInfix.java:

// Import packages

import java.util.Scanner;

import java.util.Stack;

// Declare and define the class PostfixToInfix

class PostfixToInfix {

// Determine whether the character entered is an operator or not

private boolean isOperator(char c) {

if (c == '+' || c == '-' || c == '*' || c == '/' || c == '^')

return true;

return false;

}

// Declare and define the convert()

public String convert(String postfix) {

Stack<String> s = new Stack<>();

for (int i = 0; i < postfix.length(); i++) {

char c = postfix.charAt(i);

if (isOperator(c)) {

String b = s.pop();

String a = s.pop();

s.push("(" + a + c + b + ")");

} else

s.push("" + c);

}

return s.pop();

}

// Program starts from main()

public static void main(String[] args) {

PostfixToInfix obj = new PostfixToInfix();

Scanner sc = new Scanner(System.in);

// Prompt the user to enter the postfix expression

System.out.print("Postfix : ");

String postfix = sc.next();

// Display the expression in infix expression

System.out.println("Infix : " + obj.convert(postfix));

}

}

Output:

e Console X terminated PostfixTolnfix [Java Application] C:\Program Files\Java\jrel.8.0_121\bin\javaw.exe Postfix : ABD++C-D/ .

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