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Water has a specific heat of 4.184 J/kg°C. How much energy is needed to increase the temperature of a kilogram of water by 10 degrees Celsius?

a) 418.4 J
b) 41,840 J
c) 41.84 kJ
d) 418,400 J

1 Answer

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Final answer:

To heat a kilogram of water by 10 degrees Celsius, the amount of energy needed is calculated using the specific heat capacity formula, which yields 41,840 J.

Step-by-step explanation:

The amount of energy needed to increase the temperature of a kilogram of water by 10 degrees Celsius can be calculated using the specific heat capacity formula: energy (Q) = mass (m) × specific heat (c) × temperature change (ΔT). With water's specific heat capacity being 4.184 J/g°C, the mass being 1000 grams (since 1 kg = 1000 g), and the temperature change being 10°C, we can calculate the necessary energy as follows: Q = 1000 g × 4.184 J/g°C × 10°C.

Doing the math, Q = 1000 × 4.184 × 10, which equals 41840 J. Therefore, the correct answer is (b) 41,840 J.

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