Question #c1168

1 Answer
Mar 18, 2017

"2464 J"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)ccopper=0.3850 J g1C1

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

Now, how much energy would be needed in order to increase the temperature of "715.0 g"715.0 g of copper by just 1^@"C"1C ? 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.