# Question 0ee35

Jun 29, 2015

The specific heat of your metal is 0.73"J"/("g"^@"C")#.

#### Explanation:

The equation that establishes a relationship between heat absorbed and change in temperature looks like this

$q = m \cdot c \cdot \Delta T$, where

$q$ - the heat supplied to the metal;
$m$ - the mass of the metal;
$c$ - the specific heat of the metal;
$\Delta T$ - the change in temperature, defined as the final temperature minus the initial temperature.

In your case, you know that the temperature of a 17.5-g sample of an unknown metal increased by ${3.0}^{\circ} \text{C}$ upon absorption of 38.5 J of heat.

Since the temperature increased by ${3.0}^{\circ} \text{C}$, you know that

${T}_{\text{final" - T_"initial" = 3.0^@"C}} = \Delta T$

This means that the specific heat of the metal is

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

$c = \left(38.5 \text{J")/("17.5 g" * 3.0^@"C") = 0.7333"J"/("g" ^@"C}\right)$

Rounded to two sig figs, the number of sig figs you gave for the change in temperature, the naswer will be

$c = \textcolor{g r e e n}{0.73 \text{J"/("g"^@"C}}$