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Calculate the energy required to heat 382.0 mg of iron from 6.0°C to 17.5°C. Assume the specific heat capacity of iron under these conditions is
0.449J·g⁻¹·K⁻¹. Be sure your answer has the correct number of significant digits.

Sagot :

Answer:

49.0 J

Explanation:

We need to use the specific heat equation Q=mcΔT to figure out the necessary energy, Q, to heat the grams of iron. An important step is to make sure all of the units properly cancel, which means converting all units to the ones in the specific heat capacity. In this case, since specific heat capacity is in J, g and K, we must convert all instances of temperature, mass, and energy to kelvin, grams, and joules, respectively:

  • 17.5°C - 6.0°C = 11.5°C ⇒ 11.5 + 274.15 = 285.65°K (conversion)
  • [tex]382.0mg(\frac{1g}{1000mg} ) = 0.382g[/tex] (dimensional analysis)

Now that the units have been converted, we can plug into our equation knowing that all units will cancel:

Q = (0.382) (0.449) (285.65) = 49.0 J (rounded to 3 significant figures)

(Note that units are typically written in the equation, but solely for the purpose of cancelling them to find the units of the final answer)

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