document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=826833>Question 826833</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how much heat is required to convert 50g of ice at -10degree celcius to steam at 200degree celcius? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #498436 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=498436\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How much heat is required to convert 50g of ice at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10%5Eo ALIGN=MIDDLE  ALT=\"-10%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > Celsius to steam at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%5Eo ALIGN=MIDDLE  ALT=\"200%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > Celsius?<BR>\n" );
document.write( " <BR>\n" );
document.write( "This is a problem that a science teacher (chemistry or physics) would give you.<BR>\n" );
document.write( "You need to assume that the process occurs at standard atmospheric pressure (1 atm). (The pressure at start and end is really what matters, and we should assume that is is 1 atmosphere).<BR>\n" );
document.write( "You need to calculate 5 different amounts of heat for 5 different stages of the process:<BR>\n" );
document.write( "1) the heating of ice from r 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( "2) the melting at <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( "3) the heating of the resulting liquid water 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( "4) the vaporization of the liquid water at <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;\" > , and<BR>\n" );
document.write( "5) the heating of the resulting water vapor from <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;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%5Eo ALIGN=MIDDLE  ALT=\"200%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 need data from your textbook, or from a handbook of physics (or chemistry, or engineering).<BR>\n" );
document.write( "I tried to find data, and calculate accurately, but you may have more accurate data, or be less prone to calculation mistakes, or your data may be in different units. <BR>\n" );
document.write( " <BR>\n" );
document.write( "Water, as a liquid between <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;\" > and <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( "has a \"specific heat\" of about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=calorie%2Fg%2FdegreeC ALIGN=MIDDLE  ALT=\"calorie%2Fg%2FdegreeC\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "As ice, a bit below <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<BR>\n" );
document.write( "as vapor at <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;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%5Eo ALIGN=MIDDLE  ALT=\"200%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( "it has a \"specific heat\" of about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5 ALIGN=MIDDLE  ALT=\"0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=calorie%2Fg%2FdegreeC ALIGN=MIDDLE  ALT=\"calorie%2Fg%2FdegreeC\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That is the heat it takes to increase the temperature of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1g ALIGN=MIDDLE  ALT=\"1g\"   DISABLED_style= \"max-width:90%; height:auto;\" > water by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%5Eo ALIGN=MIDDLE  ALT=\"1%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;\" >  (according to my handbook).<BR>\n" );
document.write( "(Of course, the number is a function of temperature, but it does no vary by too much).<BR>\n" );
document.write( "The heats, or \"latent heats\", of melting (for ice) and vaporization (for liquid water) are about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1440 ALIGN=MIDDLE  ALT=\"1440\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9700 ALIGN=MIDDLE  ALT=\"9700\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=calorie%2Fmol ALIGN=MIDDLE  ALT=\"calorie%2Fmol\"   DISABLED_style= \"max-width:90%; height:auto;\" > respectively (according to my handbook).<BR>\n" );
document.write( " <BR>\n" );
document.write( "So the amounts of heat required are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2850g%29%2A0.5 ALIGN=MIDDLE  ALT=\"%2850g%29%2A0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cal%2Fg ALIGN=MIDDLE  ALT=\"cal%2Fg\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280-%28-10%29%29%5Eo ALIGN=MIDDLE  ALT=\"%280-%28-10%29%29%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;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=250cal ALIGN=MIDDLE  ALT=\"250cal\"   DISABLED_style= \"max-width:90%; height:auto;\" > to heat the ice 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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2850g%2F%2218+g+%2F+mol%22%29%2A1440 ALIGN=MIDDLE  ALT=\"%2850g%2F%2218+g+%2F+mol%22%29%2A1440\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=calorie%2Fmol=4000cal ALIGN=MIDDLE  ALT=\"calorie%2Fmol=4000cal\"   DISABLED_style= \"max-width:90%; height:auto;\" >= about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4cal ALIGN=MIDDLE  ALT=\"4cal\"   DISABLED_style= \"max-width:90%; height:auto;\" > to melt the ice at <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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2850g%29%2A1 ALIGN=MIDDLE  ALT=\"%2850g%29%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cal%2Fg ALIGN=MIDDLE  ALT=\"cal%2Fg\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28100-0%29%5Eo ALIGN=MIDDLE  ALT=\"%28100-0%29%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;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5000cal ALIGN=MIDDLE  ALT=\"5000cal\"   DISABLED_style= \"max-width:90%; height:auto;\" > to heat the liquid water 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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2850g%2F%2218+g+%2F+mol%22%29%2A9700 ALIGN=MIDDLE  ALT=\"%2850g%2F%2218+g+%2F+mol%22%29%2A9700\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=calorie%2Fmol=27000cal ALIGN=MIDDLE  ALT=\"calorie%2Fmol=27000cal\"   DISABLED_style= \"max-width:90%; height:auto;\" > to vaporize the water at <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;\" > , and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2850g%29%2A0.5 ALIGN=MIDDLE  ALT=\"%2850g%29%2A0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cal%2Fg ALIGN=MIDDLE  ALT=\"cal%2Fg\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28200-100%29%5Eo ALIGN=MIDDLE  ALT=\"%28200-100%29%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;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2500cal ALIGN=MIDDLE  ALT=\"2500cal\"   DISABLED_style= \"max-width:90%; height:auto;\" > to heat the water vapor from <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;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%5Eo ALIGN=MIDDLE  ALT=\"200%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( "According to my calculation, the total energy in calories is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=250%2B4000%2B5000%2B27000%2B2500=38700 ALIGN=MIDDLE  ALT=\"250%2B4000%2B5000%2B27000%2B2500=38700\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
document.write( "\n" );
document.write( "NOTE:<BR>\n" );
document.write( "Your data may slightly different, or it may be in different units (Joules rather than calories, or Joule/g rather than calorie/mol, for example).<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );