Final answer:
To determine the mass of a water sample that cooled by 24.8°C and lost 870 J, the heat transfer formula Q = mcΔT is used. By substituting the given values and specific heat capacity of water, the calculation yields a water mass of approximately 8.39 grams.
Step-by-step explanation:
To calculate the mass of a sample of water that lost 870 J of heat and experienced a temperature drop of 24.8°C, we can use the formula for heat transfer, Q = mcΔT, where Q is the heat energy transferred, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature.
The specific heat capacity of water is commonly given as 4186 J/kg°C. By re-arranging the formula to solve for mass (m), we get:
m = Q / (cΔT)
Substituting the values provided:
m = 870 J / (4186 J/kg°C × 24.8°C)
Performing the calculation provides us with:
m = 870 / (4186 × 24.8)
m ≈ 0.00839 kg, or 8.39 g (since 1 kg = 1,000 g).
Therefore, the mass of the water sample that lost 870 J of energy and cooled by 24.8°C is approximately 8.39 grams.