No, the metal is not a pure gold since it has a different specific heat capacity (i.e 0.201 J/gºC) than that of gold (i.e 0.129 J/gºC)
How to know if the metal is a pure gold or not?
To know if the metal is pure gold or not, we calculate the specific heat capacity of the metal. This is shown below:
- Mass of metal (M) = 1.60 g
- Heat energy required (Q) = 5.8 J
- Initial temperature of metal (T₁) = 23.0 °C
- Final temperature of metal (T₂) = 41 °C
- Change in temperature (ΔT) = 41 - 23 = 18 °C
- Specific heat capacity of metal (C) = ?
Q = MCΔT
5.8 = 1.60 × C × 18
5.8 = C × 28.8
Divide both sides by 28.8
C = 5.8 / 28.8
= 0.201 J/gºC
Now, the specific heat capacity of gold is known to be 0.129 J/g°C
Thus, we can conclude that the metal is not a pure gold.
Complete question:
A 1.60 g sample of a metal that has the appearance of gold requires 5.8j of energy to change it’s temperature from 23.0 to 41 °C. Is the metal pure gold?