# Question 06850

Nov 18, 2015

0.128"J"/("g" ""^@"C")

#### Explanation:

A substance's specific heat tells you how much heat is required to heat $\text{1.0 g}$ of that substance by ${1}^{\circ} \text{C}$.

So, for example, if you need $\text{1 J}$ of heat to increase the temperature of $\text{1.0 g}$ by ${1}^{\circ} \text{C}$, then your substance has a specific heat of 1"J"/("g" ""^@"C").

Now, the equation that establishes a relationship between heat absorbed and temperature change looks like this

$\textcolor{b l u e}{q = m \cdot c \cdot \Delta T} \text{ }$, where

$q$ - the heat absorbed by the sample
$m$ - the mass of the sample
$c$ - the specific heat of the substance
$\Delta T$ - the change in temperature, defined as the final temperature minus the initial temperature

You have all the information you need to determine the metal's specific heat, so rearrange this equation and solve for $c$

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

c = "235 J"/("121.6 g" * (35.5-20.4)^@"C") = 0.12798"J"/("g" ""^@"C")

Rounded to three sig figs, the answer will be

c= color(green)(0.128"J"/("g" ""^@"C"))#