Question

Question #926ff

Answer 1

`"125,000 J"`

Explanation:

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.