Question fae70

Jul 2, 2017

$\text{795 kJ}$

Explanation:

You can switch things up a little and solve by converting the specific heat of copper from joules per gram Celsius to kilojoules per kilogram Celsius by using the two conversion factors

$\text{1 kJ" = 10^3color(white)(.)"J" " }$ and $\text{ " "1 kg" = 10^3color(white)(.)"g}$

You will end up with

0.385 color(white)(.)color(red)(cancel(color(black)("J")))/(1color(red)(cancel(color(black)("g"))) * 1^@"C") * "1 kJ"/(10^3color(red)(cancel(color(black)("J")))) * (10^3color(red)(cancel(color(black)("g"))))/"1 kg" = "0.385 kJ kg"^(-1)""^@"C"^(-1)

So, you know that in order to increase the temperature of $\text{1 kg}$ of copper by ${1}^{\circ} \text{C}$, you need to provide it with $\text{0.385 kJ}$ of heat.

You can use the specific heat of copper to figure out the amount of heat needed to increase the temperature of $\text{6.62 kg}$ of copper.

6.62 color(red)(cancel(color(black)("kg"))) * "0.385 kJ"/(1color(red)(cancel(color(black)("kg"))) * 1^@"C") = "2.549 kJ"""^@"C"^(-1)#

This means that in order to increase the temperature of $\text{6.62 kg}$ of copper by ${1}^{\circ} \text{C}$, you need to provide the sample with $\text{2.549 kJ}$ of heat.

Finally, you can use this information to determine the amount of heat needed to increase the temperature of $\text{6.62 kg}$ of copper by

${334.3}^{\circ} \text{C" - 22.5^@"C" = 311.8^@"C}$

You should get

$311.8 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{^@"C"))) * overbrace("2.549 kJ"/(1color(red)(cancel(color(black)(""^@"C")))))^(color(blue)("for 6.62 kg of copper")) = color(darkgreen)(ul(color(black)("795 kJ}}}}$

The answer is rounded to three sig figs.