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357 kJ of heat are added to 35.5 kg of water that is initially 41.2 degrees Fahrenheit. What is the water's final temperature in Fahrenheit?

A) 41.2°F
B) 82.4°F
C) 49.2°F
D) 84.4°F

1 Answer

1 vote

Final answer:

After converting the initial temperature to Celsius and the heat from kilojoules to joules, the calculated final temperature of the water is approximately 45.5°F, which is not one of the provided options.

Step-by-step explanation:

To calculate the water's final temperature after adding heat, we use the formula q = mcΔT, where q is the amount of heat added, m is the mass of the water, c is the specific heat capacity of water (which is 4.184 J/g°C), and ΔT is the change in temperature in Celsius.

First, we convert the initial temperature from Fahrenheit to Celsius using the formula ΔT°C = (ΔT°F - 32) × (5/9). For this problem, the initial temperature is 41.2°F, which converts to 5.11°C. Next, we convert the heat added from kilojoules to joules (357 kJ = 357,000 J). Now we can solve for ΔT:

ΔT = q / (mc) = 357,000 J / (35,500 g × 4.184 J/g°C) ≈ 2.42°C.

We then add this temperature change to the initial temperature in Celsius to get the final temperature in Celsius, and finally convert this back to Fahrenheit. The final temperature in Celsius is 5.11°C + 2.42°C = 7.53°C, which converts to 45.5°F.

Therefore, the correct answer is none of the provided options since the final temperature is approximately 45.5°F.

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