# What is the specific heat of an unknown substance if 2000 J of energy are required to raise the temperature of 400 grams of the substance 45 degrees Celsius?

May 28, 2016

${\text{0.1 J g"^(-1)""^@"C}}^{- 1}$

#### Explanation:

A substance's specific heat tells you how much heat is needed in order to raise the temperature of $\text{1 g}$ of that substance by ${1}^{\circ} \text{C}$.

Your tool of choice here will be this 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
$m$ - 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

In your case, the sample is said to have a mass of $\text{400 g}$. The change in temperature is said to be equal to ${45}^{\circ} \text{C}$.

You know that in order to increase the temperature of this sample by ${45}^{\circ} \text{C}$, you need to provide it with $\text{2000 J}$ of energy, which means that its specific heat will be

$q = m \cdot c \cdot \Delta T \implies c = \frac{q}{m \cdot \Delta T}$

c = "2000 J"/("400 g" * 45^@"C") = color(green)(|bar(ul(color(white)(a/a)color(black)("0.1 J g"^(-1)""^@"C"^(-1))color(white)(a/a)|)))

The answer is rounded to one sig fig.