# Question 39f99

Nov 5, 2015

Here's what I got.

#### Explanation:

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

The equation that establishes a relationship between heat absorbed and increase in temperature 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

In your case, you know that

• your metal sample has a mass of $\text{15.0 g}$
• the temperature of the sample increases from ${25.00}^{\circ} \text{C}$ to ${32.00}^{\circ} \text{C}$ after adding $\text{178.1 J}$ worth of heat to it

So, plug in your values and solve for $c$, the specific heat of the metal

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

c = "178.1 J"/("15.0 g" * (32.00 - 25.00)^@"C") = color(green)(1.70"J"/("g" ""^@"C"))#

SIDE NOTE This is a very high value to get for the specific heat of a metal, so make sure that you double-check the values you were given for heat absorbed, mass, and temperature change.

The way I see it, either the mass of the sample or the temperature change are too small, or the amount of heat absorbed is too high.