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Andrea adds 7.0 • 105 J of energy to some water by heating it from 22.0 °C up to 50.0 °C. What is the mass of the water?

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Final answer:

To calculate the mass of water Andrea heated, use the formula q = mcΔT. With the given energy (q) and the temperature change (ΔT), and knowing the specific heat capacity for water (c), we find m ≈ 5972.85 grams, or approximately 5.97285 kg.

Step-by-step explanation:

Calculating the Mass of Water from Energy Added

To find out the mass of water heated by Andrea, we can use the formula for heat energy absorbed or released by a substance, which is:

q = mcΔT

Where:

  • q is the heat energy in joules (J)
  • m is the mass in grams (g)
  • c is the specific heat capacity (For water, c = 4.184 J/g°C)
  • ΔT is the change in temperature in degrees Celsius (°C)

We can rearrange the formula to solve for m:

m = q / (cΔT)

Given:

  • q = 7.0 × 105 J
  • c = 4.184 J/g°C (specific heat of water)
  • ΔT = 50.0 °C - 22.0 °C = 28.0 °C

Thus:

m = (7.0 × 105 J) / ((4.184 J/g°C)(28.0 °C))

m = (7.0 × 105 J) / (117.152 J/g)

m ≈ 5972.85 g, or about 5.97285 kg

So, the mass of the water Andrea heated is approximately 5.97285 kilograms.

User Jay Anderson
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