# Question 926ff

Jun 8, 2017

#### Answer:

$\text{125,000 J}$

#### Explanation:

The specific heat of water tells you the amount of heat needed to increase the temperature of $\text{1 g}$ of water by ${1}^{\circ} \text{C}$.

Since water has a specific heat of ${\text{4.18 J g"^(-1)""^@"C}}^{- 1}$, you can say that in order to increase the temperature of $\text{1 g}$ of water by ${1}^{\circ} \text{C}$, you need to provide it with $\text{4.18 J}$ 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 $\text{500.0 g}$ of water by ${1}^{\circ} \text{C}$, you need to provide it with $\text{2075 J}$.

In your case, the temperature of the sample must change by

${80.0}^{\circ} \text{C" - 20.0^@"C" = 60.0^@"C}$

which implies that you must supply it with

$60 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{^@"C"))) * overbrace("2075 J"/(1color(red)(cancel(color(black)(""^@"C")))))^(color(blue)("for 500.0 g water")) = color(darkgreen)(ul(color(black)("125,000 J}}}}$

The answer is rounded to three sig figs.