A 2.6 g of a substance that looks like gold needed 9.4 J of heat energy to raise its
temperature from 20 to 38 ºC.
Is the metal pure gold?
heat=mass*specificheat*deltaTemp
solve for specific heat, then compare that value to gold
To determine if the metal is pure gold, we need to compare the specific heat capacity of gold with the specific heat capacity of the substance in question. The specific heat capacity (C) is a measure of how much heat energy is required to raise the temperature of a given amount of a substance by a certain amount.
To calculate the specific heat capacity, we can use the formula:
Q = m * C * ΔT
Where:
Q is the heat energy transferred
m is the mass of the substance
C is the specific heat capacity
ΔT is the change in temperature
Given that the substance has a mass of 2.6 g and the temperature change is from 20 ºC to 38 ºC, with 9.4 J of heat energy transferred, we can rearrange the formula to solve for C:
C = Q / (m * ΔT)
Substituting the given values:
C = 9.4 J / (2.6 g * (38 ºC - 20 ºC))
C ≈ 9.4 J / (2.6 g * 18 ºC)
C ≈ 0.204 J/gºC
Next, we need to compare this specific heat capacity with the known specific heat capacity of pure gold, which is approximately 0.129 J/gºC. If the calculated specific heat capacity matches the value for gold, it suggests that the substance is pure gold.
Comparing the calculated specific heat capacity (0.204 J/gºC) with the known specific heat capacity of gold (0.129 J/gºC), we can see that they do not match. Therefore, based on the specific heat capacity, it is likely that the substance is not pure gold.