(a) Determine the specific volume of nitrogen gas at 8.5 MPa and 139 K based on the generalized compressibility chart and compare this result with the experimental value of 0.002002 m³/kg to (b).
(b) Determine the error involved.
(R = 0.2968 kPa.m³/kg.K, Tcr=126.2 K, Pcr=3.39 MPa)

V = 0.002524m³/kg

%Error = 0.2851

Explanation:

Using the ideal gas equation, we can determine the specific volume of nitrogen as

PV = RT

V = RT/P

Given the following data:

R = 296.8j/kg.k

T = 139k

P = 8.5Mpa

Therefore, V = (296.8j/kg.k)×(139k)/8500000

V = 0.004853m³/kg

Using the compressibility chart, we can see that the compressibility factor of Nitrogen at this state is equal to 0.52. Using this, we can find out the specific volume of nitrogen to be

Z = PV/RT

0.52 = (8500000Pa)V/(296.8J/kg⋅K)(139K)

V = 0.52×296.87×139/8500000

V = 0.002524m³/kg

%Error = V(ideal)-V(actual)/V(actual)

%Error = 0.002524-0.002002/0.002002

%Error = 0.2609

Error for this compared with the actual value is

%Error = V(ideal)-V(actual)/V(actual)

%Error = (0.004853-0.002002)/0.004853

%Error = 0.2851

C++ program is explained below

Explanation:

#include <iostream>

#include <cmath>

#include <iomanip>

#include <string>

using namespace std;

int main(){

string shape;

double height;

double width;

 double radius;

const double PI = 3.1416;

double length;

cout << "Enter the shape type: (rectangle, circle, cylinder) ";

cin >> shape;

cout << endl;

if (shape == "rectangle"){

 cout << "Enter the length of the rectangle: ";

cin >> length;

cout << endl;

cout << "Enter the width of the rectangle: ";

cin >> width;

cout << endl;

cout << "Perimeter of the rectangle = "<< 2 * (length + width) << endl;

cout << "Area of the rectangle = "<< length * width << endl;

}

else if (shape == "circle"){

 cout << "Enter the radius of the circle: ";

 cin >> radius;

cout << "Area of the circle = "<< PI * pow(radius, 2.0) << endl;

 cout << "Circumference of the circle: "<< 2 * PI * radius << endl;

 cout << endl;

}

else if (shape == "cylinder")

{

cout << "Enter the height of the cylinder: ";

cin >> height;

cout << endl;

cout << "Enter the radius of the base of the cylinder: ";

cin >> radius;

cout << endl;

cout << "Surface area of the cylinder: " << 2 * PI * radius * height + 2 * PI * pow(radius, 2.0)<< endl;

cout << "Volume of the cylinder = "<< PI * pow(radius, 2.0)* height << endl;

}

else

cout << "The program does not handle " << shape << endl;

cout << fixed << showpoint << setprecision(2);

return 0;

}