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<div style="text-align: justify;"><font size="4"><span style="font-family: times new roman,times,serif; font-style: italic;">Según la ley de gases ideales existe una relación entre la presión </span><span style="font-family: times new roman,times,serif; font-style: italic; font-weight: bold;">"P",</span><span style="font-family: times new roman,times,serif; font-style: italic;"> la temperatura </span><span style="font-family: times new roman,times,serif; font-style: italic; font-weight: bold;">"T"</span><span style="font-family: times new roman,times,serif; font-style: italic;"> y el volumen </span><span style="font-family: times new roman,times,serif; font-style: italic; font-weight: bold;">"V"</span><span style="font-family: times new roman,times,serif; font-style: italic;"> del gas, dada por:</span></font><br style="font-family: times new roman,times,serif; font-style: italic;" /><br style="font-family: times new roman,times,serif; font-style: italic;" /><font size="4"> </font> <div style="text-align: center;"><font size="4"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mo»=«/mo»«mfrac»«mrow»«mi»n«/mi»«mo»·«/mo»«mi»R«/mi»«mo»§nbsp;«/mo»«mo»·«/mo»«mi»T«/mi»«/mrow»«mi»V«/mi»«/mfrac»«/math»</span><span style="font-family: times new roman,times,serif; font-style: italic;">,</span></font><br style="font-family: times new roman,times,serif; font-style: italic;" /></div><font size="4"><span style="font-family: times new roman,times,serif; font-style: italic;">donde </span><span style="font-family: times new roman,times,serif; font-style: italic; font-weight: bold;">"n" </span><span style="font-family: times new roman,times,serif; font-style: italic;">es el número de moles y </span><span style="font-family: times new roman,times,serif; font-style: italic; font-weight: bold;">"R"</span><span style="font-family: times new roman,times,serif; font-style: italic;"> es la constante universal de los gases ideales. </span></font><br style="font-family: times new roman,times,serif; font-style: italic;" /><br style="font-family: times new roman,times,serif; font-style: italic;" /><font size="4"><span style="font-family: times new roman,times,serif; font-style: italic;"> Considerando <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»n«/mi»«mo»=«/mo»«mi»#n«/mi»«/math»</span> y </span></font><font size="4"><span style="font-family: times new roman,times,serif; font-style: italic; font-weight: bold;"><span style="font-weight: bold;"><span style="font-weight: bold;"></span></span></span><span style="font-family: times new roman,times,serif; font-style: italic;"><span style="font-weight: bold;"></span>R</span></font><font size="4"><span style="font-family: times new roman,times,serif; font-style: italic;"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»=«/mo»«mn»8«/mn»«/math»</span></span><span style="font-family: times new roman,times,serif; font-style: italic;">, determina: <br /><br />¿Cuál es el volumen del gas si la presión es de <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mo»=«/mo»«mi»#P«/mi»«/math»</span> </span><span style="font-family: times new roman,times,serif; font-style: italic; font-weight: bold;">(atm)</span><span style="font-family: times new roman,times,serif; font-style: italic;"> a una temperatura de <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«mo»=«/mo»«mi»#T«/mi»«mo»§nbsp;«/mo»«mo»°«/mo»«mi»C«/mi»«/math»</span> ?</span></font><span style="color: rgb(0, 0, 0); font-family: arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"><br /><br /><font size="4"><span style="color: rgb(153, 0, 0); font-family: times new roman,times,serif; font-style: italic;">Obs.:</span></font></span><font size="4"><span style="color: rgb(153, 0, 0); font-family: times new roman,times,serif; font-size: 15px; font-style: italic; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"><br /> <font size="4">1. No utilices puntos para separar miles.</font></span></font><br /><br style="font-family: times new roman,times,serif; font-style: italic;" /><font size="4"><span style="font-family: times new roman,times,serif; font-style: italic;">{1:SA:=#V #¡Muy bien! Sigue así!} </span><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»c«/mi»«msup»«mi»m«/mi»«mn»3«/mn»«/msup»«/math»</span></font><br style="font-family: times new roman,times,serif; font-style: italic;" /></div><font size="4"><br /> </font>
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<div style="text-align: justify; font-style: italic;"><font size="4" style="font-family: times new roman,times,serif;">Solución:</font><br /><br /><font size="4" style="font-family: times new roman,times,serif;">Sabemos que la presión del gas es inversamente proporcional a su volumen, y su relación está dada por:</font><br /><br /><font size="4" style="font-family: times new roman,times,serif;"> <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»P«/mi»«mo»=«/mo»«mfrac»«mrow»«mi»n«/mi»«mo»·«/mo»«mi»R«/mi»«mo»·«/mo»«mi»T«/mi»«/mrow»«mi»V«/mi»«/mfrac»«/math»</span>.</font><br /><span style="font-family: times new roman,times,serif;"></span><br /><span style="font-family: times new roman,times,serif;"></span><font size="4" style="font-family: times new roman,times,serif;">La relación anterior indica no sólo que la presión es inversamente proporcional a su volumen, sino también que el volumen es inversamente proporcional a la presión. Para calcular el volumen del gas debemos despejar <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»V«/mi»«/math»</span>, de lo cual se obtiene la relación:</font><br /><br /><font size="4" style="font-family: times new roman,times,serif;"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»V«/mi»«mo»=«/mo»«mfrac»«mrow»«mi»n«/mi»«mo»·«/mo»«mi»R«/mi»«mo»·«/mo»«mi»T«/mi»«/mrow»«mi»P«/mi»«/mfrac»«/math»</span></font><br /><font size="4" style="font-family: times new roman,times,serif;">Reemplazando los datos en la igualdad anterior obtenemos que:</font><br /><br /><font size="4" style="font-family: times new roman,times,serif;"> <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»V«/mi»«mo»=«/mo»«mfrac»«mrow»«mi»#n«/mi»«mo»·«/mo»«mn»8«/mn»«mo»·«/mo»«mi»#T«/mi»«/mrow»«mrow»«mi»#P«/mi»«/mrow»«/mfrac»«/math»</span> <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»c«/mi»«msup»«mi»m«/mi»«mn»3«/mn»«/msup»«/math»</span>.</font><br /><font size="4" style="font-family: times new roman,times,serif;">Así, el volumen es <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»V«/mi»«mo»=«/mo»«mi»#V«/mi»«/math»</span> </font><font size="4" style="font-family: times new roman,times,serif;"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»c«/mi»«msup»«mi»m«/mi»«mn»3«/mn»«/msup»«/math»</span></font><font size="4" style="font-family: times new roman,times,serif;">.</font><br /></div>
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