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.