document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=788870>Question 788870</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At constant temperature, the atmospheric pressure p (in Pa) at an altitude h (in m) is given by Ph = Poe^(-mgh/RT), where Po is the pressure where h = 0 (atmospheric pressure at sea level). Given that Po = 1013.25 hPa (atmospheric pressure at sea level) and Ph = 900 hPa, find the value of h.\r<BR>\n" );
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document.write( "Where P0 is the atmospheric pressure at some reference level <BR>\n" );
document.write( "Ph is the atmospheric pressure at altitude h (m) above the reference level. <BR>\n" );
document.write( "m is the molecular mass of air (0.0289644 kg/mol) <BR>\n" );
document.write( "g is acceleration due to gravity (9.80665 ms-2) <BR>\n" );
document.write( "R is the gas constant constant (8.314462 JK-1mol-1) <BR>\n" );
document.write( "T is the temperature in Kelvin. In the lower altitudes temperature reduces with altitude at a rate of about 6.5 Kelvin per km of altitude.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #478670 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=478670\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5Bh%5D+=+P%5B0%5D%2Ae%5E%22%28-mgh%2FRT%29%22 ALIGN=MIDDLE  ALT=\"P%5Bh%5D+=+P%5B0%5D%2Ae%5E%22%28-mgh%2FRT%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5Bh%5D%2FP%5B0%5D=e%5E%22%28-mgh%2FRT%29%22 ALIGN=MIDDLE  ALT=\"P%5Bh%5D%2FP%5B0%5D=e%5E%22%28-mgh%2FRT%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B0%5D%2FP%5Bh%5D=e%5E%22%28mgh%2FRT%29%22 ALIGN=MIDDLE  ALT=\"P%5B0%5D%2FP%5Bh%5D=e%5E%22%28mgh%2FRT%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28P%5Bh%5D%2FP%5B0%5D%29=-mgh%2FRT ALIGN=MIDDLE  ALT=\"ln%28P%5Bh%5D%2FP%5B0%5D%29=-mgh%2FRT\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28P%5B0%5D%2FP%5Bh%5D%29=mgh%2FRT ALIGN=MIDDLE  ALT=\"ln%28P%5B0%5D%2FP%5Bh%5D%29=mgh%2FRT\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%281013.25%2F900%29=mgh%2FRT ALIGN=MIDDLE  ALT=\"ln%281013.25%2F900%29=mgh%2FRT\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=%28RT%2Fmg%29%2Aln%281013.25%2F900%29 ALIGN=MIDDLE  ALT=\"h=%28RT%2Fmg%29%2Aln%281013.25%2F900%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Assuming that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T ALIGN=MIDDLE  ALT=\"T\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the temperature at sea level, or it does not change much from 0 to h meters above sea level,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=%288.314462%2A6.5%2F%280.0289644%2A9.80665%29%29%2Aln%281013.25%2F900%29 ALIGN=MIDDLE  ALT=\"h=%288.314462%2A6.5%2F%280.0289644%2A9.80665%29%29%2Aln%281013.25%2F900%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  gives us the height in meters (because those would be the units of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=RT%2Fmg ALIGN=MIDDLE  ALT=\"RT%2Fmg\"   DISABLED_style= \"max-width:90%; height:auto;\" >} with, R, T, m, and g in the units given).<BR>\n" );
document.write( "I do not have a temperature, so I will assume <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%5EoC ALIGN=MIDDLE  ALT=\"20%5EoC\"   DISABLED_style= \"max-width:90%; height:auto;\" > (293 kelvins)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=%288.314462%2A293%2F%280.0289644%2A9.80665%29%29%2Aln%281013.25%2F900%29=1017%29 ALIGN=MIDDLE  ALT=\"h=%288.314462%2A293%2F%280.0289644%2A9.80665%29%29%2Aln%281013.25%2F900%29=1017%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the height is about 1,000 meters. </SPAN>\n" );
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