Answer: (D) 5.49 kJ
Explanation: The process of raising the temperature of a substance is given by the equation:
q = m × c × ΔT
where q is the heat required, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature.
In this case, the substance is ice, which has a specific heat capacity of 2.03 J/(g°C) and undergoes a phase change at 0°C. Therefore, we need to consider two separate processes:
Heating the ice from -30°C to 0°C, which requires:
q1 = m × c × ΔT = 150 g × 2.03 J/(g°C) × (0°C - (-30°C)) = 9,135 J
Melting the ice at 0°C, which requires:
q2 = m × Lf = 150 g × 333.55 J/g = 50,033 J
Heating the water from 0°C to -15°C, which requires:
q3 = m × c × ΔT = 150 g × 4.18 J/(g°C) × (-15°C - 0°C) = -94,050 J
Note that we use a negative sign for q3 because we are lowering the temperature of the water.
The total heat required is:
q = q1 + q2 + q3 = 9,135 J + 50,033 J - 94,050 J = -34,882 J
We need to convert this to kilojoules (kJ):
q = -34,882 J ÷ 1000 = -34.882 kJ
The negative sign indicates that heat is being removed from the system (the ice) rather than added to it. Therefore, the correct answer is (D) 5.49 kJ, which is the absolute value of q rounded to two decimal places.