To determine which piece of ice has the most thermal energy, we need to calculate the thermal energy for each piece. This is given by the formula for thermal energy:
[tex]\[ Q = m \cdot c \cdot \Delta T \][/tex]
where [tex]\( Q \)[/tex] is the thermal energy, [tex]\( m \)[/tex] is the mass, [tex]\( c \)[/tex] is the specific heat capacity of ice (approximately [tex]\( 2.1 \, \text{J/g}^\circ\text{C} \)[/tex]), and [tex]\( \Delta T \)[/tex] is the change in temperature.
We have four pieces of ice to evaluate:
1. A 10,000 g ice sculpture at -1°C.
2. A 10,000 g ice sculpture at -2°C.
3. A 10 g ice cube at -1°C.
4. A 10 g ice cube at -3°C.
Using the formula, we calculate:
1. For the 10,000 g ice sculpture at -1°C:
[tex]\[
Q_1 = 10000 \, \text{g} \cdot 2.1 \, \text{J/g}^\circ\text{C} \cdot (0 - (-1))^\circ\text{C} = 10000 \, \text{g} \cdot 2.1 \, \text{J/g}^\circ\text{C} \cdot 1^\circ\text{C} = 21,000 \, \text{J}
\][/tex]
2. For the 10,000 g ice sculpture at -2°C:
[tex]\[
Q_2 = 10000 \, \text{g} \cdot 2.1 \, \text{J/g}^\circ\text{C} \cdot (0 - (-2))^\circ\text{C} = 10000 \, \text{g} \cdot 2.1 \, \text{J/g}^\circ\text{C} \cdot 2^\circ\text{C} = 42,000 \, \text{J}
\][/tex]
3. For the 10 g ice cube at -1°C:
[tex]\[
Q_3 = 10 \, \text{g} \cdot 2.1 \, \text{J/g}^\circ\text{C} \cdot (0 - (-1))^\circ\text{C} = 10 \, \text{g} \cdot 2.1 \, \text{J/g}^\circ\text{C} \cdot 1^\circ\text{C} = 21 \, \text{J}
\][/tex]
4. For the 10 g ice cube at -3°C:
[tex]\[
Q_4 = 10 \, \text{g} \cdot 2.1 \, \text{J/g}^\circ\text{C} \cdot (0 - (-3))^\circ\text{C} = 10 \, \text{g} \cdot 2.1 \, \text{J/g}^\circ\text{C} \cdot 3^\circ\text{C} = 63 \, \text{J}
\][/tex]
Comparing the calculated thermal energies:
- The 10,000 g ice sculpture at -1°C has 21,000 J.
- The 10,000 g ice sculpture at -2°C has 42,000 J.
- The 10 g ice cube at -1°C has 21 J.
- The 10 g ice cube at -3°C has 63 J.
Among these values, the ice sculpture of 10,000 g at -2°C has the highest thermal energy at 42,000 J.
Therefore, the piece of ice with the most thermal energy is:
[tex]\[ \boxed{\text{B. A 10,000 g ice sculpture at -2}^{\circ}\text{C}} \][/tex]
