Question

Question #c1168

Answer 1

`"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.