This is the 25<sup>th</sup> series of my "Thermodynamics Review Problems for Mechanical Engineering Students". If you've missed the previous series you may try scrolling this blog and head over to the "Curriculum". This series features a review problem for Three-process Thermodynamic cycles for which two months ago I made two blogs about this matter. See, <a href="https://steemit.com/education/@josephace135/three-process-thermodynamic-cycles-with-review-problem-english-units-or-part-1">Part 1</a> and <a href="https://steemit.com/education/@josephace135/three-process-thermodynamic-cycles-or-review-problem-si-units-or-part-2-of-2">Part 2</a>.

<h2>Review Problem</h2>

<div class=”text-justify”>A three-process cycle operating with <code>5 kg<sub>m</sub></code> of air as the working substance has the following processes: constant volume (1 -> 2); constant pressure (2 -> 3); and constant temperature (3 -> 1). Given that <code>P<sub>1</sub> = 100 kPa</code>, <code>T<sub>1</sub> = 300°K</code> and <code>V<sub>1</sub> / V<sub>3</sub> = 6</code>, determine the heat added in <code>kJ</code>.</div>

<h4>Solution</h4>

<div class="text-justify">For this review problem, the very first thing to do is to **draw the P-V diagram** of the said three-process cycle. After creating the P-V diagram of the said cycle, by inspection we can say that the heat that is being added to the cycle is done during the isometric process which is literally process 1 -> 2 and is the only one providing a positive sign heat which means heat that is being added. As we proceed to the computation, the first thing to obtain is the pressure at the start of isothermal process which is <code>P<sub>3</sub></code>, and it can only be obtain using the pressure and volume relations during an isothermal process. By using the provided ratio for volumes <code>V<sub>1</sub></code> and <code>V<sub>3</sub></code>, we’ve found out that the <code>P<sub>3</sub></code> is equal to <code>600 kPa</code>. Additionally, since process 2 -> 3 is an isobaric one or constant pressure, <code>P<sub>2</sub></code> is also equal to <code>600 kPa</code>. Next thing to obtain is the temperature at the end of isometric process, for which we can obtain it using the pressure and temperature ratio during a constant volume process. By using the relation, we’ve found out that <code>1800°K</code>. And since we now have both <code>T<sub>1</sub></code> and <code>T<sub>2</sub></code>, we can now finally solve for the heat that is being added to the cycle and we’ve found out that it is equal to <code>5389.5 kJ</code>.</div>

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  <th><center>Computation for:</center></th>
  <th><center>Screenshots</center></th>
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  <td><center>Pressure versus volume diagram of  3-process cycle, <code>P-V</code></center></td>
  <td><center><img src="https://cdn.steemitimages.com/DQmfSMqtvUSBnpY1ztA6j3KZURBt24HVkNr3jEV8Cu1k1xo/image.jpg" alt="image.jpg" /><br/></center></td>
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  <td><center>Pressure at the start of isothermal process (3 -> 1), <code>P<sub>3</sub></code></center></td>
  <td><center><img src="https://cdn.steemitimages.com/DQmajGTZkr19Ph4fJBFWHa7bCwiDXdWc7HsaHBLEXMSzET2/blob" alt="" /><br/></center></td>
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  <td><center>Temperature at the end of isometric process (1 -> 2), <code>T<sub>2</sub></code></center></td>
  <td><center><img src="https://cdn.steemitimages.com/DQmQ3twg7Qe9Hiot8WnLyCW5CseVrjFypqTYfv5vyVmzFyi/blob" alt="" /><br/></center></td>
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  <td><center>Heat added, <code>Q<sub>A</sub></code></center></td>
  <td><center><img src="https://cdn.steemitimages.com/DQmbvCAdhEKBMgkH8yAJGzA7x9JWc9y2EUKMUbm7nUKv4JR/blob" alt="" /><br/></center></td>
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<center><img src="https://cdn.steemitimages.com/DQmP17gc5E9DQZ3dt5D1rnSHHEyg4QQB3zFjY65j7FbZRPL/divider_orange_1.png" alt="divider_orange_1.png" /><br/></center>

<h3>Curriculum</h3>

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  <td><center><a href="https://steemit.com/steempress/@josephace135/thermodynamicsreviewproblemsformechanicalengineeringstudentsseries1-wn7uq6kvpg">Series 1</a></center></td>
  <td><center><a href="https://steemit.com/steempress/@josephace135/thermodynamicsreviewproblemsformechanicalengineeringstudentsseries2-6lcsrltr2w">Series 2</a></center></td>
  <td><center><a href="https://steemit.com/steempress/@josephace135/thermodynamicsreviewproblemsformechanicalengineeringstudentsseries3-vh52owp6gu">Series 3</a></center></td>
  <td><center><a href="https://steemit.com/steempress/@josephace135/thermodynamicsreviewproblemsformechanicalengineeringstudentsseries4-xtvspq68gq">Series 4</a></center></td>
  <td><center><a href="https://steemit.com/steempress/@josephace135/thermodynamicsreviewproblemsformechanicalengineeringstudentsseries5-06375eqnov">Series 5</a></center></td>
  <td><center><a href="https://steemit.com/steempress/@josephace135/thermodynamicsreviewproblemsformechanicalengineeringstudentsseries6-uya95fv8an">Series 6</a></center></td>
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  <td><center><a href="https://steemit.com/steempress/@josephace135/thermodynamicsreviewproblemsformechanicalengineeringstudentsseries7-k910i3ghfg">Series 7</a></center></td>
  <td><center><a href="https://steemit.com/problem/@josephace135/thermodynamicsreviewproblemsformechanicalengineeringstudentsseries8-8vn7gpc0lu">Series 8</a></center></td>
  <td><center><a href="https://steemit.com/steempress/@josephace135/thermodynamicsreviewproblemsformechanicalengineeringstudentsseries9-gh5o5citu5">Series 9</a></center></td>
  <td><center><a href="https://steemit.com/steemstem/@josephace135/thermodynamicsreviewproblemsformechanicalengineeringstudentsseries10-i712b335mx">Series 10</a></center></td>
  <td><center><a href="https://steemit.com/steemstem/@josephace135/thermodynamicsreviewproblemsformechanicalengineeringstudentsseries11-x0fk3w4pxr">Series 11</a></center></td>
  <td><center><a href="https://steemit.com/steemstem/@josephace135/thermodynamicsreviewproblemsformechanicalengineeringstudentsseries11-o8de4f1rek">Series 12</a></center></td>
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  <td><center><a href="https://steemit.com/steemstem/@josephace135/thermodynamicsreviewproblemsformechanicalengineeringstudentsseries13-ip4l5yp67z">Series 13</a></center></td>
  <td><center><a href="https://steemit.com/steemstem/@josephace135/thermodynamicsreviewproblemsformechanicalengineeringstudentsseries14-jvsypysxiw">Series 14</a></center></td>
  <td><center><a href="https://steemit.com/steemstem/@josephace135/thermodynamicsreviewproblemsformechanicalengineeringstudentsseries15ottocycle-d9ry2hyzjh">Series 15</a></center></td>
  <td><center><a href="https://steemit.com/steemstem/@josephace135/mechanicalengineeringstudentsseries16ottocycleagain-0n3agi9xw6">Series 16</a></center></td>
  <td><center><a href="https://steemit.com/steemiteducation/@josephace135/thermodynamicsreviewproblemsformechanicalengineeringstudentsseries17ottocycleforthe4thtime-crpx2tyc6k">Series 17</a></center></td>
  <td><center><a href="https://steemit.com/steemiteducation/@josephace135/thermodynamicsreviewproblemsformechanicalengineeringstudentsseries18finalseriesforottocycle-fug9dd4l96">Series 18</a></center></td>
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  <td><center><a href="https://steemit.com/steemiteducation/@josephace135/thermodynamicsreviewproblemsformechanicalengineeringstudentsseries19dieselcycle-k1pzc9f1kh">Series 19</a></center></td>
  <td><center><a href="https://steemit.com/steemiteducation/@josephace135/thermodynamicsreviewproblemsformechanicalengineeringstudentsseries20dieselcycleagain-an2gckz085">Series 20</a></center></td>
  <td><center><a href="https://steemit.com/steemiteducation/@josephace135/thermodynamicsreviewproblemsformechanicalengineeringstudentsseries21dieselcycleforthethirdtime-0lahpmrbhh">Series 21</a></center></td>
  <td><center><a href="https://steemit.com/steemiteducation/@josephace135/thermodynamicsreviewproblemsformechanicalengineeringstudentsseries21fourthseriesfordieselcycle-sz1xvs6vm5">Series 22</a></center></td>
  <td><center><a href="https://steemit.com/steemiteducation/@josephace135/thermodynamicsreviewproblemsformechanicalengineeringstudentsseries23fifthseriesfordieselcycle-2dhs6ktaof">Series 23</a></center></td>
  <td><center><a href="https://steemit.com/steemiteducation/@josephace135/thermodynamicsreviewproblemsformechanicalengineeringstudentsseries24sixthseriesfordieselcycle-osemnn0vcg">Series 24</a></center></td>
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</table>

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<h3>Reference</h3>

<ol>
<li>PIPE - PROBLEM SET #3 by Alcorcon Engineering Review Center</li>
<li>Sta. Maria, H. [1990] 2012. <em>Thermodynamics 1</em>. Mandaluyong City: National Bookstore Inc..</li>
</ol>

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<center><sub>Computations and screenshots are made by the author.</sub></center>

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<center><sub>Special thanks to @jbeguna04 for designing the GIF and divider photos.</sub></center>