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vesna_86 [32]
4 years ago
10

The temperature of a gas is related to its absolute pressure and specific volume through T = 3.488pv, where T, p, and v are expr

essed in their standard SI units. Consider a gas at 100 kPa and 1 m3/kg. (a) Estimate the change in temperature (ΔT) using Taylor's theorem if the state of the gas changes to 101 kPa and 1.01 m3/kg. (b) Compare your estimate with the exact change in temperature.
Engineering
1 answer:
tangare [24]4 years ago
7 0

Answer:

0.425kPA \approx 0.43kPa

Explanation:

In order to solve the problem we must resort to Taylor's approximations in which it is possible to obtain an approximation through a polynomial function.

For the particular case we proceed to make a linear approach.

Our values are defined as,

T = 3.488pv \rightarrowRelation of temperature, pressure and volume

T_1 = 350K \rightarrow Initial Temperature

v_1 = 1m^3/Kg \rightarrow Specific Volume

T_2 = 355K \rightarrow Final Temperature

v_2 = 1.01m^3/kh \rightarrow Final Specific Volume

The previous equation can be expressed as function of pressure, i.e,

P = \frac{T}{3.488v}

We can differentiate the expression in function of temperature and the specific volume, then

Temperature:

\frac{dP}{dT} = \frac{1}{3.488v}

Volume

\frac{dP}{dv} = -\frac{T}{3.488v^2}

PART A) Then the total change of the pressure is given by,

\Delta P = \frac{dP}{dT} + \frac{dP}{dv}

\Delta P =  \frac{1}{3.488v}(T_2-T_1)-\frac{T}{3.488v^2}(v_2-v_1)

Replacing the values given, we have

\Delta P =  \frac{1}{3.488(1.01)}(355-350)-\frac{355}{3.488(1.01)^2}(1.01-1)

\Delta P = 0.43kPa

PART B) Now we can calculate the exact change in pressure through the general equation, that is

\Delta P = \frac{1}{3.488}(\frac{T_2}{v_2}-\frac{T_1}{v_1})

Replacing the values we have:

\Delta P =  \frac{1}{3.488}(\frac{355}{1.01}-\frac{350}{1})

\Delta P = 0.425kPA

We can conclude that the approximation by Taylor's theorem is close to the value calculated by the general expression.

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Please add comments to your program to explain it. Thank you!
Step2247 [10]

Answer / Explanation:

(1) We should first understand that the input filename are passed in as the first command arguments at command line, respectively.

To do this, we import the data file:

So we have,

import java.io.*;

/**

*  Makes a copy of a file.  The original file and the name of the

*  copy must be given as command-line arguments.  In addition, the

*  first command-line argument can be "-f"; if present, the program

*  will overwrite an existing file; if not, the program will report

*  an error and end if the output file already exists.  The number

*  of bytes that are copied is reported.

*/

public class CopyFile {

  public static void main(String[] args) {

     String sourceName;   // Name of the source file,  

                          //    as specified on the command line.

     String copyName;     // Name of the copy,  

                          //    as specified on the command line.

     InputStream source;  // Stream for reading from the source file.

     OutputStream copy;   // Stream for writing the copy.

     boolean force;  // This is set to true if the "-f" option

                     //    is specified on the command line.

     int byteCount;  // Number of bytes copied from the source file.

     

     /* Get file names from the command line and check for the  

        presence of the -f option.

(2)   If the command line is not one

        of the two possible legal forms, print an error message and  

        end this program. */

   

     if (args.length == 3 && args[0].equalsIgnoreCase("-f")) {

        sourceName = args[1];

        copyName = args[2];

        force = true;

     }

     else if (args.length == 2) {

        sourceName = args[0];

        copyName = args[1];

        force = false;

     }

     else {

        System.out.println(

                "Usage:  java CopyFile <source-file> <copy-name>");

        System.out.println(

                "    or  java CopyFile -f <source-file> <copy-name>");

        return;

     }

     

     /* Create the input stream.  If an error occurs, end the program. */

     

     try {

        source = new FileInputStream(sourceName);

     }

     catch (FileNotFoundException e) {

        System.out.println("Can't find file \"" + sourceName + "\".");

        return;

     }    

     /* If the output file already exists and the -f option was not

        specified, print an error message and end the program. */

   

     File file = new File(copyName);

     if (file.exists() && force == false) {

         System.out.println(

              "Output file exists.  Use the -f option to replace it.");

         return;  

    }      

     /* Create the output stream.  If an error occurs, end the program. */

     try {

        copy = new FileOutputStream(copyName);

     }

     catch (IOException e) {

        System.out.println("Can't open output file \"" + copyName + "\".");

        return;

     }

     

   (3)   /* Copy one byte at a time from the input stream to the output

        stream, ending when the read() method returns -1 (which is  

        the signal that the end of the stream has been reached).  If any  

        error occurs, print an error message.  Also print a message if  

        the file has been copied successfully.  */  

     byteCount = 0;

     

     try {

        while (true) {

           int data = source.read();

           if (data < 0)

              break;

           copy.write(data);

           byteCount++;

        }

        source.close();

        copy.close();

        System.out.println("Successfully copied " + byteCount + " bytes.");

     }

     catch (Exception e) {

        System.out.println("Error occurred while copying.  "

                                  + byteCount + " bytes copied.");

        System.out.println("Error: " + e);

     }    

  }  // end main()  

} // end class CopyFile

8 0
4 years ago
What is the difference between a Datum and a Datum Feature? a) A Datum and Datum Feature are synonymous. b) A Datum is theoretic
aliina [53]

Difference between Datum and Datum feature is<em> 'Datum is theoretical and Datum feature is real'. </em>

Option: (b)

<u>Explanation:</u>

A Datum is a perfect plane, line, point or surface but only occurs theoretically.

However a Datum Feature is fully based on a tangible surface, axis or point on a part where that theoretical datum is located.

The reason behind in this is they are not equal to each other because the 'part surface' is never 100% perfect.

The important functional features of the Datum is controlled during measurements.

7 0
3 years ago
Stream Piracy – Kaaterskill, NY. Check and double-click the Problem 15 folder. The dark blue and orange streams highlight the pr
baherus [9]

Answer:

b. The pirating streams are eroding headwardly to intersect more of the other streams’ drainage basins, causing water to be diverted down their steeper gradients.

Explanation:

From the Kaaterskill NY 15 minute map (1906), this shows two classic examples of stream capture.

The Kaaterskill Creek flow down the east relatively steep slopes into the Hudson River Valley. While, the Gooseberry Creek is a low gradient stream flowing down the west direction which in turn drains the higher parts of the Catskills in this area.

However, there is Headward erosion of Kaaterskill Creek which resulted to the capture of part of the headwaters of Gooseberry Creek.

The evidence for this is the presence of "barbed" (enters at obtuse rather than acute angle) tributary which enters Kaaterskill Creek from South Lake which was once a part of the Gooseberry Creek drainage system.

It should be noted again, that there is drainage divide between the Gooseberry and Kaaterskill drainage systems (just to the left of the word Twilight) which is located in the center of the valley.

As it progresses, this divide will then move westward as Kaaterskill captures more and more of the Gooseberry system.

5 0
3 years ago
Evaluate each of the following to three significant figures and express each answer in SI units using an appropriate prefix: (a)
Sonbull [250]

Answer:

Explanation:

(a)

\frac{354 mg \, 45 km}{0.0356 kN} = 354 mg \times \frac{1 kg}{10^6 mg} \times 45 km \times \frac{10^3m}{1 km} \times \frac{1}{0.0356 kN} \times \frac{1 kN}{10^3 N} = 0.447 \frac{kg \, m}{N}

(b)

0.00453 Mg \times 201 ms = 0.00453 Mg \times \frac{10^3 kg}{1 Mg} \times 201 ms \times \frac{1 s}{10^3 ms} = 0.911 kg \, s

(c)

\frac{435 MN}{23.2 mm} = 435 MN \times \frac{10^6 N}{1 MN} \times \frac{1}{23.2 mm}  \times \frac{10^3 mm}{1 m} = 18.75 \times 10^9 \frac{N}{m} = 18.75 \frac{GN}{m}

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shusha [124]

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Hope it help you friend

6 0
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