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
298J=4.30*cgold*(Tf-22)
cgold has to be in units of J/gC
solve for Tf in Celcius units.
To find the final temperature of the gold nugget, we need to use the specific heat capacity formula:
q = m * c * ΔT
Where:
q = heat absorbed or released by a substance (in this case, 298 J)
m = mass of the substance (4.30 g)
c = specific heat capacity of the substance (for gold, it is 0.129 J/g°C)
ΔT = change in temperature (final temperature - initial temperature)
We can rearrange the formula to solve for ΔT:
ΔT = q / (m * c)
Plugging in the given values:
ΔT = 298 J / (4.30 g * 0.129 J/g°C)
To simplify the calculation, let's convert the mass from grams (g) to kilograms (kg):
ΔT = 298 J / (0.00430 kg * 0.129 J/g°C)
Now we can solve for ΔT:
ΔT = 298 J / (0.000555 kg * 0.129 J/g°C)
ΔT = 298 J / 0.000071595 J/°C
ΔT = 4,156.82 °C
Since the initial temperature was 22.0°C, we can find the final temperature:
Final temperature = Initial temperature + ΔT
Final temperature = 22.0°C + 4,156.82°C
Final temperature = 4,178.82°C
Therefore, the final temperature of the gold nugget is approximately 4,178.82°C.