A 0.52g sample of metal that looks like gold requires 1.65 J of energy to change its temperature from 25.0°C to 40°C. Is this metal pure gold?

Question

Serenity Allen · Accepted Answer

No, it's not.

The idea here is that you need to use the information provided by the problem to calculate the specific heat of the unknown material. A quick comparison with the listed value for the specific heat of gold will determine if the unknown material is indeed pure gold or not. So, your tool of choice here will be the equation #color(blue)(ul(color(black)(q = m * c * DeltaT)))# Here Rearrange to solve for #c# #q = m * c * DeltaT implies c = q/(m * DeltaT)# Plug in your values to find #c = "1.65 J"/("0.52 g" * (40.0 - 25.0)^@"C") = "0.212 J g"^(-1)""^@"C"^(-1)# Now, gold has a specific heat of about #c_"gold" = "0.129 J g"^(-1)""^@"C"^(-1)# https://tutor.hix.ai which means that your unknown material is not pure gold. The fact that its specific heat is higher than that of pure gold implies that it also contains materials that have a higher specific heat than that of gold.

Avery Adams · Answer

undefined No, the metal is not pure gold. Gold has a specific heat capacity of 0.129 J/g°C, so it would require less energy to change its temperature compared to the given metal.