A 4.30 g nugget of pure gold absorbed 298 J of heat. The initial temperature was 22.0°C. What was the final temperature?
°C
To solve this problem, we can use the heat equation:
Q = m * c * ΔT
Where:
Q is the heat absorbed by the gold nugget (in joules),
m is the mass of the gold nugget (in grams),
c is the specific heat capacity of gold (in J/g°C),
ΔT is the change in temperature (final temperature - initial temperature).
First, let's calculate the heat capacity of the gold nugget:
Q = m * c * ΔT
298 J = 4.30 g * c * ΔT
Next, we need to find the specific heat capacity (c) of gold. The specific heat capacity is the amount of heat required to raise the temperature of 1 gram of a substance by 1 degree Celsius.
The specific heat capacity of gold is approximately 0.129 J/g°C.
Now, we can substitute the values into the equation:
298 J = 4.30 g * 0.129 J/g°C * ΔT
Let's solve for ΔT:
ΔT = 298 J / (4.30 g * 0.129 J/g°C)
ΔT ≈ 54.827°C
Finally, to find the final temperature, we add the change in temperature (54.827°C) to the initial temperature (22.0°C):
Final Temperature = Initial Temperature + ΔT
Final Temperature ≈ 22.0°C + 54.827°C
Final Temperature ≈ 76.827°C
Therefore, the final temperature of the gold nugget is approximately 76.827°C.