document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186021>Question 1186021</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The volume of a 6 x 12-ft tank is 339.3 cu ft. It contains air at 200 psig and 85°F. How many 1-cu ft drums can be filled to 50 psig and 80°F if it is assumed that the air temperature in the tank remains at 85°F? The drums have been sitting around in the atmosphere which is at 14.7 psia and 80°F. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849483 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849483\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to calculate the number of drums that can be filled:\r<BR>\n" );
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document.write( "**1. Convert psig to psia:**\r<BR>\n" );
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document.write( "* Tank pressure: 200 psig + 14.7 psia = 214.7 psia<BR>\n" );
document.write( "* Drum pressure: 50 psig + 14.7 psia = 64.7 psia\r<BR>\n" );
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document.write( "**2. Convert temperatures to absolute Rankine:**\r<BR>\n" );
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document.write( "* Tank temperature: 85°F + 460 = 545°R<BR>\n" );
document.write( "* Drum temperature: 80°F + 460 = 540°R\r<BR>\n" );
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document.write( "**3. Use the ideal gas law to find the mass of air in the tank:**\r<BR>\n" );
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document.write( "The ideal gas law is PV = mRT, where:\r<BR>\n" );
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document.write( "* P = pressure<BR>\n" );
document.write( "* V = volume<BR>\n" );
document.write( "* m = mass<BR>\n" );
document.write( "* R = specific gas constant for air (1716 ft-lbf/slug-°R)<BR>\n" );
document.write( "* T = temperature\r<BR>\n" );
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document.write( "Rearranging to solve for mass: m = PV / RT\r<BR>\n" );
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document.write( "m = (214.7 psia * 144 in²/ft² * 339.3 ft³) / (1716 ft-lbf/slug-°R * 545 °R)<BR>\n" );
document.write( "m ≈ 4.79 slugs\r<BR>\n" );
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document.write( "**4. Use the ideal gas law again to find the volume the air will occupy at drum conditions:**\r<BR>\n" );
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document.write( "We'll use the same formula, but this time we're solving for V: V = mRT / P\r<BR>\n" );
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document.write( "V = (4.79 slugs * 1716 ft-lbf/slug-°R * 540 °R) / (64.7 psia * 144 in²/ft²)<BR>\n" );
document.write( "V ≈ 2216.7 ft³\r<BR>\n" );
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document.write( "**5. Calculate the number of drums that can be filled:**\r<BR>\n" );
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document.write( "Number of drums = Volume of air at drum conditions / Volume per drum<BR>\n" );
document.write( "Number of drums = 2216.7 ft³ / 1 ft³/drum<BR>\n" );
document.write( "Number of drums ≈ 2217 drums\r<BR>\n" );
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document.write( "**Therefore, approximately 2217 drums can be filled.**<BR>\n" );
document.write( " </SPAN>\n" );
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