Question #c1168

1 Answer
Mar 18, 2017

Answer:

#"2464 J"#

Explanation:

The key to this problem is the specific heat of the metal.

You know that copper has a specific heat of

#c_"copper" = "0.3850 J g"^(-1)""^@"C"^(-1)#

This tells you that in order to increase the temperature of #"1 g"# of copper by #1^@"C"#, you need to provide it with #"0.3850 J"# of heat.

Now, how much energy would be needed in order to increase the temperature of #"715.0 g"# of copper by just #1^@"C"# ? Use the specific heat as a conversion factor to get

#715.0 color(red)(cancel(color(black)("g"))) * overbrace("0.3850 J"/(1color(red)(cancel(color(black)("g"))) * 1^@"C"))^(color(blue)("the specific heat of copper")) = "275.275 J"^@"C"^(-1)#

Since you know that you need #"275.275 J"# of heat in order to increase the temperature of #"715.0 g"# of copper by #1^@"C"#, you can say that in order to increase its temperature by

#22.46^@"C" - 13.51^@"C" = 8.95^@"C"#

you will need to provide

#8.95 color(red)(cancel(color(black)(""^@"C"))) * "275.275 J"/(1color(red)(cancel(color(black)(""^@"C")))) = color(darkgreen)(ul(color(black)("2464 J")))#

The answer is rounded to four sig figs.