To determine the percentage (%) of the gold bar that melts, we need to calculate the mass of the gold bar and the heat required to melt it. By dividing the heat required to melt the gold by the total heat added, we can find the percentage of the gold bar that melts i.e. = 0.24%.
To determine the percentage (%) of the gold bar that melts, we need to calculate the amount of heat needed to melt the gold and compare it to the total heat added.
First, we need to find the specific heat capacity of gold. In Exercise 7.3.3, it is stated that gold has a specific heat of 0.129 J/g °C. Using this information, we can calculate the mass of the gold bar. In the problem, 1,377 J of heat are needed to increase the temperature of the gold by 99.9°C. So, we divide the heat by the specific heat capacity to get the mass: 1,377 J ÷ 0.129 J/g °C = 10.7 g.
Now that we know the mass of the gold bar, we can determine the amount of heat needed to melt it. The heat required to melt a substance is given by the formula: Q = m × ΔH, where Q is the heat, m is the mass, and ΔH is the heat of fusion. For gold, the heat of fusion is 63.7 J/g. So, the heat needed to melt the gold bar is: Q = 10.7 g × 63.7 J/g = 681.59 J.
Finally, we can calculate the percentage of the gold bar that melts by dividing the heat required to melt it by the total heat added and multiplying by 100: (681.59 J ÷ 284,000 J) × 100 = 0.24%