document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1085178>Question 1085178</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A) Equal masses of water at 20 Celsius and iron at 40 Celsius are put together in a Styrofoam cup. The water has a specific heat of 1 cal/g C and the iron has a specific heat of 0.113 cal/g C. What do you think the final temp will be of both the water and the iron in the Styrofoam cup? Show your work.\r<BR>\n" );
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document.write( "B) What would happen if you combined equal masses of liquid water at 10 C with ice at 0 C? What do you think the final temp might be? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #699261 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=699261\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A) If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the mass, in grams, of each component (water and iron,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the final temperature of both the water and the iron, in degrees Celsius,<BR>\n" );
document.write( "the heat gained by the water, in calories, is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2A1%2A%28x-20%29 ALIGN=MIDDLE  ALT=\"m%2A1%2A%28x-20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the heat lost by the iron is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2A0.113%2A%2840-x%29 ALIGN=MIDDLE  ALT=\"m%2A0.113%2A%2840-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "working in a Styrofoam cup the heat gained from or lost to the environment is negligible, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2A1%2A%28x-20%29=m%2A0.113%2A%2840-x%29 ALIGN=MIDDLE  ALT=\"m%2A1%2A%28x-20%29=m%2A0.113%2A%2840-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-20=0.113%2A%2840-x%29 ALIGN=MIDDLE  ALT=\"x-20=0.113%2A%2840-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Solving:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-20=0.113%2A%2840-x%29 ALIGN=MIDDLE  ALT=\"x-20=0.113%2A%2840-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-20=4.52-0.113x%29 ALIGN=MIDDLE  ALT=\"x-20=4.52-0.113x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B0.113x=20%2B4.52%29 ALIGN=MIDDLE  ALT=\"x%2B0.113x=20%2B4.52%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.113x=24.52%29 ALIGN=MIDDLE  ALT=\"1.113x=24.52%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=24.52%2F1.113%29 ALIGN=MIDDLE  ALT=\"x=24.52%2F1.113%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=22.03%28rounded%29 ALIGN=MIDDLE  ALT=\"x=22.03%28rounded%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "B) It takes 79.72 calories to melt 1 gram of ice.<BR>\n" );
document.write( "That is called enthalpy of fusion, or heat of fusion, or latent heat of fusion.<BR>\n" );
document.write( "It is a lot of heat, so ice can take a lot of heat away from anything it touches.<BR>\n" );
document.write( "Can 1 gram of ice take enough heat from 1 gram of water to cool it from 10 degrees to 0 degrees?<BR>\n" );
document.write( "Let's see.<BR>\n" );
document.write( "Cooling 1 gram of water from 10 degrees to 0 degrees (Celsius) takes only<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281gram%29%2A%2810degrees%29%2A1 ALIGN=MIDDLE  ALT=\"%281gram%29%2A%2810degrees%29%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=calorie%2F%28gram%2Adegree%29=10degrees ALIGN=MIDDLE  ALT=\"calorie%2F%28gram%2Adegree%29=10degrees\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, if you mix 1 gram of water 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;\" ><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 1 gram of 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( "you get water 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;\" > with a slightly smaller amount of ice floating in it, all of it 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( " </SPAN>\n" );
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