# Question #0c3b6

Jun 21, 2016

$q = 22.5 J$

#### Explanation:

First, it is necessary to make sure the copper is not undergoing any phase changes during the heating process. To check this, look at the melting point of copper: 1084.62 °C.

Since both the final and initial temperatures are below the melting point of copper, the copper will remain solid throughout the process, and it is not necessary to calculate any heat of fusion.

Next, the following equation can be used to solve for the amount of heat required to elevate the temperature of the copper:

$q = m {c}_{p} \Delta T$

Where $q$ is heat, ${c}_{p}$ is the heat capacity of copper at constant pressure, and $\Delta T$ is the change in temperature.

${c}_{p}$ is a physical property of copper and can be looked up in a table. The heat capacity of copper is:

${c}_{p} = 0.39 k \frac{J}{k g \cdot K}$

Finally, simply plug the values into the equation and solve for $q$.

$q = m {c}_{p} \Delta T$
$q = \left(0.00450 k g\right) \cdot \left(0.39 k \frac{J}{k g \cdot K}\right) \cdot \left(32.0 C - 19.2 C\right)$

$q = 0.0225 k J$ or $22.5 J$

Note: It is not necessary to convert to Kelvin since the difference in temperature is the same as it is in Celsius.