A 4.30 g nugget of pure gold absorbed 293 J of heat. The initial temperature was 23.0°C. What was the final temperature?
To determine the final temperature, we can use the heat capacity equation:
Q = m * c * ΔT
where:
Q is the amount of heat absorbed (in joules),
m is the mass of the substance (in grams),
c is the specific heat capacity of the substance (in J/g°C), and
ΔT is the change in temperature (in °C).
Given:
Q = 293 J
m = 4.30 g
Initial temperature (T₁) = 23.0°C
We need to rearrange the equation to solve for ΔT:
ΔT = Q / (m * c)
First, we need to find the specific heat capacity of gold:
The specific heat capacity of gold is 0.128 J/g°C.
Now, substituting the given values into the equation:
ΔT = 293 J / (4.30 g * 0.128 J/g°C)
ΔT = 293 J / (0.5504 J/°C)
ΔT ≈ 532.70°C
To find the final temperature, we add the change in temperature (ΔT) to the initial temperature (T₁):
Final temperature (T₂) = T₁ + ΔT
T₂ = 23.0°C + 532.70°C
T₂ ≈ 555.70°C
Therefore, the final temperature of the gold nugget is approximately 555.70°C.