Question #0b2c1

1 Answer
Feb 5, 2017

Answer:

#"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")))#