Added Luis's English solution of 5.5.3

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+ <title>Savchenko Solutions</title>
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+ content="A website with solutions to physics problems from Savenko Textbook" />
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+ <header>
+ <h2>Solutions of Savchenko Physics Textbook</h2>
+ <p class="author">
+ Aliaksandr Melnichenka <br/>
+ October 2023
+ </p>
+ </header>
+
+ <main>
+ <article>
+ <h3 id="back-link"><a href="../">$\leftarrow$Back</a></h3>
+
+ <h4>Statement</h4>
+ <p>
+ $5.5.3$
+ For diminishing isothermally $n$ times the volume of gas in a cylinder with piston, over this piston is putted a load of mass $m$. What load should be added such that the volume of gas decreases isothermally $k$ times more?
+ </p>
+ <center>
+ <figure>
+ <img src="statement.png"
+ loading="lazy" alt="5.5.3" width="200" />
+ <figcaption>
+ For problem 5.5.3
+ </figcaption>
+ </figure>
+ </center>
+ <h4>Solution</h4>
+ <p class="TxtSolutions">
+ Applying Newton's Second Law...
+ </p>
+ <p class="TxtSolutions">
+ Initially, considering a massless piston
+ </p>
+ <center>
+ $P_0 = P_a \;(1)$
+ </center>
+ When load of mass $m$ is putted over
+ <center>
+ $PS=mg+P_aS \;(2)$
+ </center>
+ <p class="TxtSolutions">
+ After the addition of the another load,
+ </p>
+ <center>
+ $P'S=(m+\Delta m)g+P_aS \;(3)$
+ </center>
+ <p class="TxtSolutions">
+ From Boyle-Mariotte Law
+ </p>
+ <center>
+ $P_0V_0 = P\frac{V_0}{n}$
+ </center>
+ <center>
+ $P_0 = \frac{P}{n} \;(4)$
+ </center>
+ <p class="TxtSolutions">
+ Substituting $(2)$ into $(3)$, according to $(1)$ and separating $P_a$
+ </p>
+ <center>
+ $P_a = \frac{mg}{S(n-1)} \;(5)$
+ </center>
+ <p class="TxtSolutions">
+ Applying Boyle-Mariotte Law again
+ </p>
+ <center>
+ $P\frac{V_0}{n}=P'\frac{V_0}{nk}$
+ </center>
+ <center>
+ $P=\frac{P'}{k} \;(6)$
+ </center>
+ <p class="TxtSolutions">
+ Substituting $(2)$ and $(3)$ into $(6)$ and developing algebraically
+ </p>
+ <center>
+ $\left(\frac{mg}{S}+P_a\right)(k-1)=\frac{\Delta mg}{S} \;(7)$
+ </center>
+ <p class="TxtSolutions">
+ Putting $(5)$ into $(7)$ and separating $\Delta m$
+ </p>
+ <center>
+ $\boxed{\Delta m=m\frac{(k-1)n}{(n-1)}}$
+ </center>
+ <p class="TxtSolutions" style="text-align: right; font-style: italic; font-size: 14;">
+ BSc. Luis Daniel Fernández Quintana<br>
+ Physics Department (FCNE)<br>
+ Universidad de Oriente, Cuba<br>
+ </p>
+ </article>
+ </main>
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