Question #926ff

The specific heat of water tells you the amount of heat needed to increase the temperature of #"1 g"# of water by #1^@"C"#.

Since water has a specific heat of #"4.18 J g"^(-1)""^@"C"^(-1)#, you can say that in order to increase the temperature of #"1 g"# of water by #1^@"C"#, you need to provide it with #"4.18 J"# of heat.

This means that for your

#0.500 color(red)(cancel(color(black)("kg"))) * (10^3color(white)(.)"g")/(1color(red)(cancel(color(black)("kg")))) = "500.0 g"#

sample of water, you will have

#500.0 color(red)(cancel(color(black)("g"))) * "4.18 J"/(1color(red)(cancel(color(black)("g"))) * 1^@"C") = "2075 J"^@"C"^(-1)#

This means that in order to increase the temperature of #"500.0 g"# of water by #1^@"C"#, you need to provide it with #"2075 J"#.

In your case, the temperature of the sample must change by

#80.0^@"C" - 20.0^@"C" = 60.0^@"C"#

which implies that you must supply it with

#60 color(red)(cancel(color(black)(""^@"C"))) * overbrace("2075 J"/(1color(red)(cancel(color(black)(""^@"C")))))^(color(blue)("for 500.0 g water")) = color(darkgreen)(ul(color(black)("125,000 J")))#

The answer is rounded to three sig figs.