Question

Question #0b2c1

Answer 1

`"1.1 kJ"`

Explanation:

In order to be able to answer this question, you must know the value of the specific heat of water, which you'll find listed as

`c_"water" = "4.18 J g"^(-1)""^@"C"^(-1)`

The specific heat of a substance tells you the amount of heat needed in order to increase the temperature of `"1 g"` of that substance by `1^@"C"`.

In this case, you need `"4.18 J"` in order to increase the temperature of `"1 g"` of water by `1^@"C"`.

You know that the temperature of the water must change by

`DeltaT = 65^@"C" - 10^@"C" = 55^@"C"`

so start by calculating the amount of heat needed to increase the temperature of `"1 g"` of water by `55^@"C"`.

`55color(red)(cancel(color(black)(""^@"C"))) * "4.18 J"/("1 g" * 1color(red)(cancel(color(black)(""^@"C")))) = "229.9 J g"^(-1)`

Your sample has a mass of

`0.5 color(red)(cancel(color(black)("kg"))) * (10^3"g")/(1color(red)(cancel(color(black)("kg")))) = "500 g"`

which means that the amount of heat needed to increase its temperature by `55^@"C"` will be

`500color(red)(cancel(color(black)("g"))) * "229.9 J"/(1color(red)(cancel(color(black)("g")))) = "114950 J"`

I'll leave the answer rounded to two sig figs and expressed in kilojoules, but do keep in mind that you only have one significant figure for the mass of the sample

`color(darkgreen)(ul(color(black)("heat needed = 1.1 kJ")))`