Final answer:
To calculate the heat lost by the aluminum sample, use the equation Q = mcΔT. The aluminum sample must lose approximately 135 J of heat for its temperature to change from 550.0°C to 540.0°C.
Step-by-step explanation:
To calculate the heat lost by the aluminum sample, we can use the equation Q = mcΔT, where Q is the heat, m is the mass of the sample, c is the specific heat capacity of aluminum, and ΔT is the change in temperature.
In this case, the mass of the sample is 15.0 grams, the specific heat capacity of aluminum is 0.897 J/g°C, and the change in temperature is -10.0°C (from 550.0°C to 540.0°C).
Using these values, we can calculate the heat lost by the sample as follows:
Q = (15.0 g)(0.897 J/g°C)(-10.0°C)
= -134.55 J
≈ -135 J
Therefore, the aluminum sample must lose approximately 135 J of heat for its temperature to change from 550.0°C to 540.0°C.