Answer:
The ice pack must extract 15.75 kJ of thermal energy from the water to reduce its temperature by 15°C.
Step-by-step explanation:
The amount of thermal energy (heat) required to change the temperature of a substance is given by the equation:
Q = m * c * ΔT
Where Q is the amount of thermal energy, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature of the substance.
In this problem, we know the mass of the water (m = 0.25 kg), the specific heat capacity of water (c = 4.2 kJ/(kg°C)), and the change in temperature (ΔT = -15°C, since the temperature is decreasing). We want to find the amount of thermal energy (Q) that the ice pack must extract from the water to achieve this temperature change.
Plugging in the values, we get:
Q = (0.25 kg) * (4.2 kJ/(kg°C)) * (-15°C)
Q = -15.75 kJ
Since the temperature is decreasing, the thermal energy (heat) must be negative. Therefore, the ice pack must extract 15.75 kJ of thermal energy from the water to reduce its temperature by 15°C.