Question

1. a jeweler wants to create a ring for his wife from a gold bar with mass $1.4 \times 10^{-5}$ kg and is at room temperature $25 \\, ^\circ\text{c}$.\

a. what is the specific heat of gold?\
b. the melting point of gold is $1063 \\, ^\circ\text{c}$. what is the temperature change of the gold bar?\
c. how much heat does the jeweler need to add to the gold block in order to bring it to its melting point $1063 \\, ^\circ\text{c}$?

Explanation:

Step1: Recall gold's specific heat

The specific heat of gold is a known constant from physical properties of materials.

Step2: Calculate temperature change

Subtract initial temp from melting point.
$\Delta T = T_{final} - T_{initial} = 1063^\circ\text{C} - 25^\circ\text{C}$

Step3: Calculate required heat

Use heat formula $Q = mc\Delta T$, substitute values.
$Q = 1.4\times10^{-5}\ \text{kg} \times 129\ \frac{\text{J}}{\text{kg}\cdot^\circ\text{C}} \times 1038^\circ\text{C}$

Answer:

a. $129\ \frac{\text{J}}{\text{kg}\cdot^\circ\text{C}}$
b. $1038^\circ\text{C}$
c. $1.90\ \text{J}$ (rounded to two decimal places)