Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
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]
[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]
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.