Question

The specific heat of gold is 0.129 J/g C. A king gets sold a gold crown but he's unsure if it's pure gold. He takes the crown which weighs 1,130 grams, heats it to 98.8 C, and then places it in 1.34 L of water with a starting point of 25.83 C. The final temperature of the water is 27.84 C. What is the specific heat of the crown and is it pure gold?

Answer 1

We can use the formula:

Q = mcΔT

where Q is the heat absorbed or released, m is the mass, c is the specific heat, and ΔT is the change in temperature.

First, let's calculate the heat absorbed by the crown:

Q1 = mcΔT

Q1 = (1130 g)(0.129 J/g C)(98.8 C - 25.83 C)

Q1 = 107,776.6 J

Next, let's calculate the heat released by the crown into the water:

Q2 = mcΔT

Q2 = (m)(c)(ΔT)

Q2 = (1340 g)(4.184 J/g C)(27.84 C - 25.83 C)

Q2 = 11096.64 J

Since Q1 = -Q2 (heat lost by the crown is equal to heat gained by the water),

mcΔT = -mcΔT

We can then solve for the specific heat of the crown:

c = -(Q2/mΔT)

c = -(11096.64 J)/(1130 g)(27.84 C - 25.83 C)

c = 0.131 J/g C

The specific heat of pure gold is 0.129 J/g C, and the specific heat of the crown is 0.131 J/g C. Since the specific heat of the crown is slightly higher than that of pure gold, it is possible that the crown is not pure gold. However, other factors such as impurities or alloying metals can also affect the specific heat, so further analysis would be necessary to confirm if the crown is pure gold.