# Question 0b2c1

Feb 5, 2017

$\text{1.1 kJ}$

#### 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

${c}_{\text{water" = "4.18 J g"^(-1)""^@"C}}^{- 1}$

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

In this case, you need $\text{4.18 J}$ in order to increase the temperature of $\text{1 g}$ of water by ${1}^{\circ} \text{C}$.

You know that the temperature of the water must change by

$\Delta T = {65}^{\circ} \text{C" - 10^@"C" = 55^@"C}$

so start by calculating the amount of heat needed to increase the temperature of $\text{1 g}$ of water by ${55}^{\circ} \text{C}$.

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 ${55}^{\circ} \text{C}$ 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

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{\text{heat needed = 1.1 kJ}}}}$