# How many joules of heat energy would be required to raise the temperature of 150.0 g of aluminum from 23°C to 150°C?

## The specific heat capacity of aluminum is .90 $J$/g*°C.

May 29, 2016

$\text{17,000 J}$

#### Explanation:

Your tool of choice here will be the following equation

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} q = m \cdot c \cdot \Delta T \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$, where

$q$ - the amount of heat gained / lost
$m$ - the mass of the sample
$c$ - the specific heat of the substance
$\Delta T$ - the change in temperature, defined as the difference between the final temperature and the initial temperature

The problem provides you with all the information that you need in order to determine the amount of heat, $q$, needed.

In your case, the change in temperature will be

$\Delta T = {150}^{\circ} \text{C" - 23^@"C" = 127^@"C}$

All you have to do now is plug in your values into the above equation and solve for $q$

$q = 150.0 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{g"))) * 0.90"J"/(color(red)(cancel(color(black)("g"))) * color(red)(cancel(color(black)(""^@"C")))) * 127color(red)(cancel(color(black)(""^@"C}}}}$

$q = \text{17,145 J}$

Rounded to two sig figs, the answer will be

"amount of heat needed" = color(green)(|bar(ul(color(white)(a/a)color(black)("17,000 J")color(white)(a/a)|)))