# Question #0b2c1

##### 1 Answer

#### 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

In this case, you need

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

#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

#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")))#