Question

1. as of january 2023, a one - kilogram gold bar is selling for roughly $62,000 while a one - kilogram silver bar is selling for roughly $875.

a. what is the heat required to raise a gold bar by one degree celsius?
b. what is the heat required to raise a silver bold by one degree celsius?
c. calculate the energy difference to raise each bar by one degree celsius.

Explanation:

Step1: Recall specific heat formula

The formula for heat required is $Q = mc\Delta T$, where $m$ = mass, $c$ = specific heat capacity, $\Delta T$ = temperature change.

Step2: Define known values for gold

$m = 1000\ \text{g}$, $c_{\text{gold}} = 0.129\ \text{J/g}^\circ\text{C}$, $\Delta T = 1^\circ\text{C}$

Step3: Calculate heat for gold

$Q_{\text{gold}} = 1000 \times 0.129 \times 1 = 129\ \text{J}$

Step4: Define known values for silver

$m = 1000\ \text{g}$, $c_{\text{silver}} = 0.235\ \text{J/g}^\circ\text{C}$, $\Delta T = 1^\circ\text{C}$

Step5: Calculate heat for silver

$Q_{\text{silver}} = 1000 \times 0.235 \times 1 = 235\ \text{J}$

Step6: Calculate energy difference

$\Delta Q = |Q_{\text{silver}} - Q_{\text{gold}}| = |235 - 129| = 106\ \text{J}$

Answer:

a. $129\ \text{J}$
b. $235\ \text{J}$
c. $106\ \text{J}$