Final answer:
The piece of ice gains a total of 52.08 kJ of heat as it melts and warms to room temperature.
Step-by-step explanation:
To calculate the amount of heat gained by the piece of ice, we need to consider two steps:
Step 1: Bring the ice from -11°C to 0°C. The heat gained in this step can be calculated using the specific heat capacity of ice:
q₁ = mass × specific heat capacity × change in temperature
q₁ = 145.87 g × 2.09 J/g°C × (0 - (-11))°C
q₁ = 3296.13 J
= 3.30 kJ
Step 2: Melt the ice at 0°C. The heat gained in this step can be calculated using the heat of fusion:
q₂ = mass × heat of fusion
q₂ = 145.87 g × 334 J/g = 48784.58 J
= 48.78 kJ
The total amount of heat gained by the ice is the sum of q₁ and q₂:
Total heat gained = q₁ + q₂
= 3.30 kJ + 48.78 kJ
= 52.08 kJ