This is the 13<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 two problems relating to <a href="https://steemit.com/education/@josephace135/overview-on-thermodynamic-processes-with-review-problem-english-units-polytropic-process">Polytropic Process</a> for which the first review problem requires us to compute the change in internal energy (∆U) and the heat that is being transferred under the given conditions and lastly, the second review problem requires us to compute the work produce in expanding the air in a closed piston-cylinder device. Without much ado, let’s start solving these review problems.

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<h3>Review Problem 1</h3>

<blockquote>
  Air is compressed polytropically in a cylinder according to <code>PV<sup>2</sup> = C</code>. The work required is <code>180 kJ per kg</code>. Determine the following:
  - change in internal energy (∆U); and
  - heat transferred (Q).

</blockquote>

<h4>Solution</h4>

<ul>
<li>Change of Internal Energy (∆U)
In computing for the change in internal energy (∆U), the very first thing to obtain is the change in temperature (∆T) since we are provided with the work that is required to polytropically compress the air at a polytropic index of 2 (n = 2). We can obtain the change in temperature (∆T) since work can be expressed in the formula shown below.
<center><img src="https://cdn.steemitimages.com/DQmRdgsmRH2riLiYEBbBwkyxJxmrgRJFqeRN35ogAu6pqVd/blob" alt="" /><br/></center>
Simplifying the equation to make it looking for the change in temperature (∆T), we’ve found out that the change in temperature is equal to <code>- 627.18°K</code> for which the negative sign indicates that the air experienced a decrease in its temperature. Take note that gas constant of air is equal to <code>0.287 kJ per kg per °K</code>.
<center><img src="https://cdn.steemitimages.com/DQmUfa1hA5yZ4FqRpk8PYJshf8tQ7VVdsLjYwcHQHjqtPQN/blob" alt="" /><br/></center>
Finally, the change in internal energy (∆U) is equal to <code>-450.69 kJ per kg</code>; as shown in the computation below. Additionally, the specific heat capacity of air at constant volume is equal to <code>0.7186 kJ per kg per °K</code>.
<center><img src="https://cdn.steemitimages.com/DQmNUQkLataTYziYiDzhCKog4GaKrGA57LUjCdsqscb59qX/blob" alt="" /><br/></center></li>
<li>Heat Transferred (Q)
Since heat (Q) is just equal to the sum of change in internal energy (∆U) and the work; the work for compressing the air polytropically is equal to <code>-270.69 kJ per kg</code>. That negative sign indicates that the heat is being transferred/rejected to the surroundings.
<center><img src="https://cdn.steemitimages.com/DQmU8pAtzFp49CZS2Boq8dEjEXfgdQN7xnAe6EipjZQQ464/blob" alt="" /><br/></center></li>
</ul>

<h3>Review Problem 2</h3>

<blockquote>
  Air is expanded from <code>1 MPa and 327°C</code> to <code>200 kPa</code> in a closed piston-cylinder device executing <code>PV<sup>1.2</sup> = C</code> process. The work produce during this process in <code>kJ per kg</code> is:

</blockquote>

<h4>Solution</h4>

In computing for the work being executed by the closed piston-cylinder device as it expands the air, the very first thing to obtain is the final temperature (T<sub>2</sub>) since we are provided with both the initial and final pressures of the air. Before computing for the final temperature (T<sub>2</sub>) lets first convert <code>327°C</code> to degree Kelvin, wherein we will just at 273 and expressed in degree Kelvin, so <code>327°C</code> is equal to <code>600°K</code>. Then the final temperature (T<sub>2</sub>) is obtain using the temperature and pressure relation at polytropic process and by doing so, we’ve found out that it is equal to <code>458.83°K</code>.
<center><img src="https://cdn.steemitimages.com/DQmVN8pdgtKUTMgG644kse3o9TnqakGkDiVM3wEunPSzoCi/blob" alt="" /><br/> </center>
Finally we can now compute for the work that is produced upon the expansion of air and using the formula being used in problem number 1; we’ve found out that the work produced in expanding the air polytropically is equal to <code>202.58 kJ per kg</code>.
<center><img src="https://cdn.steemitimages.com/DQmRE8AjJgzC3u46BpQVqNm8FxCBKDGw5yXvBNycmpYyfkk/blob" alt="" /><br/> </center>

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<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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<center><img src="https://cdn.steemitimages.com/DQmP17gc5E9DQZ3dt5D1rnSHHEyg4QQB3zFjY65j7FbZRPL/divider_orange_1.png" alt="divider_orange_1.png" /><br/></center>

<h3>Reference</h3>

<ul>
<li>PIPE - PROBLEM SET #2 by Alcorcon Engineering Review Center</li>
</ul>

<center><img src="https://cdn.steemitimages.com/DQmP17gc5E9DQZ3dt5D1rnSHHEyg4QQB3zFjY65j7FbZRPL/divider_orange_1.png" alt="divider_orange_1.png" /><br/></center>

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

<center><img src="https://cdn.steemitimages.com/DQmVfb2EhoTJxQYu1isLMZ1nyGZy3KJDZ4UX9mqBcqAU5Ko/giface_final_footer.gif" alt="giface_final_footer.gif" /><br/></center>

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