Final answer:
The amount of heat energy needed to convert 150 grams of ice at -15°C to ice at -63°C is 54,968.25 J.
Step-by-step explanation:
To find the amount of heat energy needed to convert 150 grams of ice at -15°C to ice at -63°C, we need to consider the temperature change and the phase change of the ice. We can use the formula:
Q = m * c * ΔT + m * ΔH_f
Where Q is the total heat energy, m is the mass of the ice, c is the specific heat capacity of ice, ΔT is the change in temperature, and ΔH_f is the heat of fusion of ice.
First, we need to calculate the heat energy needed to change the temperature of the ice from -15°C to 0°C:
Q1 = 150 g * 2.09 J/g°C * (0 - (-15))°C = 4,935 J
Next, we need to calculate the heat energy needed to change the phase of the ice from solid to liquid:
Q2 = 150 g * 333.55 J/g = 50,033.25 J
The total heat energy needed is the sum of Q1 and Q2:
Q = 4,935 J + 50,033.25 J = 54,968.25 J
Therefore, the amount of heat energy needed to convert 150 grams of ice at -15°C to ice at -63°C is 54,968.25 J.