Answer :
Final answer:
The final temperature of aluminum after adding 75.9 J of heat to a 106 g piece initially at 24.5°C is calculated to be approximately 25.3°C, which does not match any of the options provided.
None of the option is correct.
Explanation:
To calculate the final temperature of the aluminum after adding heat, we use the formula for heat transfer: Q = mcΔT, where Q is the heat added, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. With the given specific heat of aluminum (900 J/kg·°C), we can find the increase in temperature and add it to the initial temperature to get the final temperature.
First, convert the mass of aluminum from grams to kilograms:
m = 106 g = 0.106 kg
Next, rearrange the formula to solve for ΔT:
ΔT = Q / (mc)
Now we plug in the values:
ΔT = 75.9 J / (0.106 kg·900 J/kg·°C) = 0.8411°C
Finally, add this temperature change to the initial temperature:
Final temperature = 24.5°C + 0.8411°C = approximately 25.3°C
None of the provided options match this result, so it is possible there may be a mismatch between the question and the options or a calculation error in the given options.
None of the option is correct.
