The specific heat of gold is 0.031 calories/gram°C and the specific heat of silver is 0.057 calories/gram°C. If equal amounts of each metal are exposed to equal heating, which will heat up faster?
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To determine which metal will heat up faster, you need to know their specific heat values and the mass of each metal.
The specific heat of gold is given as 0.031 calories/gram°C, and the specific heat of silver is given as 0.057 calories/gram°C.
Since equal amounts of each metal are exposed to equal heating, we can assume that the mass of both metals is the same.
Let's assume the mass of both gold and silver is 'm' grams.
To calculate the heat absorbed by each metal, we can use the formula:
Heat = Mass × Specific Heat × Temperature Change
Let's assume the initial temperature of both metals is the same, so the temperature change for both metals will also be the same.
Now, we can compare the heat absorbed by each metal using the formula:
Heat_absorbed_by_gold = m × 0.031 × temperature_change
Heat_absorbed_by_silver = m × 0.057 × temperature_change
Since the mass and temperature change are the same for both metals, we can compare the specific heats directly.
Given that the specific heat of silver (0.057) is greater than the specific heat of gold (0.031), silver will heat up faster.
Therefore, if equal amounts of each metal are exposed to equal heating, silver will heat up faster than gold.
Why not choose a convenient temperature gain (say 1 degree C) and a convenient mass (say 1 g) and calculate the heat required to raise the T by that amount?
q = mass x specific heat x delta T
q = 1 x 0.031 x 1 and
q = 1 x 0.057 x 1.
Which requires more heat to raise 1 g of the metal 1 C? So the OTHER one will heat up faster.