document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=840064>Question 840064</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A chemist measured the pressure of a gas in atmospheres at different temperatures in °C:<BR>\n" );
document.write( "Temp (°C) -136 -25 0 25 100 273<BR>\n" );
document.write( "Pressure(atm) 0.50 0.91 1.00 1.09 1.37 2.00<BR>\n" );
document.write( "Can you predict the temperature at which the pressure would equal zero? Please explain how you got to your conclusion. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #505924 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=505924\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The data shows that pressure is a linear function of temperature.<BR>\n" );
document.write( " <BR>\n" );
document.write( "PLOTTING THE DATA POINTS to get a graph, you realize that pressure is a linear function of temperature. Your teacher may expect you to plot the data, and \"eyeball\" a line that goes through all the points.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C300%2C-300%2C300%2C-0.5%2C2.5%2C%0D%0Agrid%280%29%2C%0D%0Ared%28circle%28-136%2C0.5%2C3%29%29%2Cred%28circle%28-25%2C0.91%2C3%29%29%2C%0D%0Ared%28circle%280%2C1%2C3%29%29%2Cred%28circle%2825%2C1.09%2C3%29%29%2C%0D%0Ared%28circle%28100%2C1.37%2C3%29%29%2Cred%28circle%28273%2C2%2C3%29%29%2C%0D%0Agreen%28line%28-273%2C0%2C300%2C2.1%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > From the graph you realize that the points are almost perfectly aligned, so it is a linear function.<BR>\n" );
document.write( "From the line you may be able to estimate that the point with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (pressure equal zero atmosphere) corresponds to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-273 ALIGN=MIDDLE  ALT=\"x=-273\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-273%5Eo ALIGN=MIDDLE  ALT=\"-273%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > ).<BR>\n" );
document.write( "You do not need to read that from the graph. Knowing that<BR>\n" );
document.write( "as the temperature increases from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%5Eo ALIGN=MIDDLE  ALT=\"0%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=273%5Eo ALIGN=MIDDLE  ALT=\"273%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "the pressure increases by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%221.00+atm%22 ALIGN=MIDDLE  ALT=\"%221.00+atm%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%221.00+atm%22 ALIGN=MIDDLE  ALT=\"%221.00+atm%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%222.00+atm%22 ALIGN=MIDDLE  ALT=\"%222.00+atm%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "you would figure out that<BR>\n" );
document.write( "as the temperature decreases from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%5Eo ALIGN=MIDDLE  ALT=\"0%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-273%5Eo ALIGN=MIDDLE  ALT=\"-273%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "the pressure will decrease by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%221.00+atm%22 ALIGN=MIDDLE  ALT=\"%221.00+atm%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%221.00+atm%22 ALIGN=MIDDLE  ALT=\"%221.00+atm%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%220.00+atm%22 ALIGN=MIDDLE  ALT=\"%220.00+atm%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "It could also be that your teacher expects you to calculate the slope, using two points, and write the linear function, to find the x intercept.<BR>\n" );
document.write( "Using the points for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%5Eo ALIGN=MIDDLE  ALT=\"0%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-273%5Eo ALIGN=MIDDLE  ALT=\"-273%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope=%281.37-1.00%29%2F100=0.37 ALIGN=MIDDLE  ALT=\"slope=%281.37-1.00%29%2F100=0.37\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "We know the y-intercept is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1.00 ALIGN=MIDDLE  ALT=\"y=1.00\"   DISABLED_style= \"max-width:90%; height:auto;\" >, since the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > (pressure) for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0%5Eo ALIGN=MIDDLE  ALT=\"x=0%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%221.00+atm%22 ALIGN=MIDDLE  ALT=\"%221.00+atm%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > , so the linear function is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0.37x%2B%221.00%22 ALIGN=MIDDLE  ALT=\"y=0.37x%2B%221.00%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pressure=0.37temperature%2B%221.00%22 ALIGN=MIDDLE  ALT=\"pressure=0.37temperature%2B%221.00%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Hopefully you are not expected to go into statistic calculations.<BR>\n" );
document.write( " <BR>\n" );
document.write( "QUICK ANSWER, WITHOUT PLOTTING, AND WITHOUT A CALCULATOR:<BR>\n" );
document.write( "You see that as the temperature increases by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%5Eo ALIGN=MIDDLE  ALT=\"25%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees<BR>\n" );
document.write( "(from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-25%5Eo ALIGN=MIDDLE  ALT=\"-25%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%5Eo ALIGN=MIDDLE  ALT=\"0%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > or from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%5Eo ALIGN=MIDDLE  ALT=\"0%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%5EoC ALIGN=MIDDLE  ALT=\"25%5EoC\"   DISABLED_style= \"max-width:90%; height:auto;\" > ),<BR>\n" );
document.write( "the pressure increases by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9atm ALIGN=MIDDLE  ALT=\"9atm\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and for a temperature increases 4 times as large<BR>\n" );
document.write( "( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%5Eo ALIGN=MIDDLE  ALT=\"100%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > increase, from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%5Eo ALIGN=MIDDLE  ALT=\"0%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%5Eo ALIGN=MIDDLE  ALT=\"100%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > ),<BR>\n" );
document.write( "the pressure increases by about 4 times as much, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=37atm ALIGN=MIDDLE  ALT=\"37atm\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The rate of increase (the slope of the line) seems to be about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.37 ALIGN=MIDDLE  ALT=\"0.37\"   DISABLED_style= \"max-width:90%; height:auto;\" > atmosphere per degree.<BR>\n" );
document.write( "You also see that the increase in pressure for a temperature increase of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=273%5Eo ALIGN=MIDDLE  ALT=\"273%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%221.00+atm%22 ALIGN=MIDDLE  ALT=\"%221.00+atm%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and for half as large a change in temperature (from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-136%5Eo ALIGN=MIDDLE  ALT=\"-136%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%5Eo ALIGN=MIDDLE  ALT=\"0%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > ),<BR>\n" );
document.write( "the pressure increases by half as much, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.50atm ALIGN=MIDDLE  ALT=\"0.50atm\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "You could calculate the slope from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%5Eo ALIGN=MIDDLE  ALT=\"0%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=273%5Eo ALIGN=MIDDLE  ALT=\"273%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > to verify that it is also about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.37 ALIGN=MIDDLE  ALT=\"0.37\"   DISABLED_style= \"max-width:90%; height:auto;\" > , but that takes time.<BR>\n" );
document.write( "nowing that<BR>\n" );
document.write( "as the temperature increases from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%5Eo ALIGN=MIDDLE  ALT=\"0%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=273%5Eo ALIGN=MIDDLE  ALT=\"273%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "the pressure increases by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%221.00+atm%22 ALIGN=MIDDLE  ALT=\"%221.00+atm%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%221.00+atm%22 ALIGN=MIDDLE  ALT=\"%221.00+atm%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%222.00+atm%22 ALIGN=MIDDLE  ALT=\"%222.00+atm%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "you would figure out that<BR>\n" );
document.write( "as the temperature decreases from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%5Eo ALIGN=MIDDLE  ALT=\"0%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-273%5Eo ALIGN=MIDDLE  ALT=\"-273%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "the pressure will decrease by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%221.00+atm%22 ALIGN=MIDDLE  ALT=\"%221.00+atm%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%221.00+atm%22 ALIGN=MIDDLE  ALT=\"%221.00+atm%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%220.00+atm%22 ALIGN=MIDDLE  ALT=\"%220.00+atm%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "without ever using a calculator or pencil and paper.<BR>\n" );
document.write( " <BR>\n" );
document.write( "NOTE:<BR>\n" );
document.write( "As a non-famous chemist of the 20th-21st centuries, I would not extrapolate that far out of the data range to draw a conclusion.<BR>\n" );
document.write( "Besides, they taught me that in the 9th grade, in physics and chemistry classes.<BR>\n" );
document.write( "A physicist in the 1700's would draw a conclusion from such limited data as he could obtain at the time. If he was a famous and respected scientist, people would eventually believe him, and his conclusion would become a law of physics named after him that would be included in physics and chemistry textbooks. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );