Answer :
To determine how much energy is needed to raise the temperature of 25 grams of tin compared to 25 grams of gold, each by 10 degrees Celsius, we can use the formula for calculating heat energy:
[tex]\[ Q = m \cdot C \cdot \Delta T \][/tex]
where:
- [tex]\( Q \)[/tex] is the heat energy,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( C \)[/tex] is the specific heat capacity,
- [tex]\( \Delta T \)[/tex] is the change in temperature.
Given the specific values:
- For tin (Sn): [tex]\( C _{ Sn } = 0.240 \frac{ J }{ g \cdot^{\circ} C } \)[/tex]
- For gold (Au): [tex]\( C _{ Au } = 0.129 \frac{ J }{ g \cdot ^{\circ} C } \)[/tex]
- Mass ([tex]\( m \)[/tex]): 25 grams
- Change in temperature ([tex]\( \Delta T \)[/tex]): 10 degrees Celsius
Let's calculate the energy needed for both substances:
### Energy required for tin (Sn):
[tex]\[ Q _{ Sn } = m \cdot C _{ Sn } \cdot \Delta T \][/tex]
[tex]\[ Q _{ Sn } = 25 \, g \cdot 0.240 \, \frac{ J }{ g \cdot ^{\circ} C } \cdot 10 \, ^{\circ} C \][/tex]
[tex]\[ Q _{ Sn } = 25 \cdot 0.240 \cdot 10 \][/tex]
[tex]\[ Q _{ Sn } = 60 \, J \][/tex]
### Energy required for gold (Au):
[tex]\[ Q _{ Au } = m \cdot C _{ Au } \cdot \Delta T \][/tex]
[tex]\[ Q _{ Au } = 25 \, g \cdot 0.129 \, \frac{ J }{ g \cdot ^{\circ} C } \cdot 10 \, ^{\circ} C \][/tex]
[tex]\[ Q _{ Au } = 25 \cdot 0.129 \cdot 10 \][/tex]
[tex]\[ Q _{ Au } = 32.25 \, J \][/tex]
### Comparing the energies:
- Energy required for tin (Sn): 60 J
- Energy required for gold (Au): 32.25 J
From these calculations, we can see that the energy required to raise the temperature of 25 grams of tin by 10 degrees Celsius is 60 J, while the energy required for the same mass and temperature increase of gold is 32.25 J. Therefore, tin requires more energy than gold to achieve the same increase in temperature.
### Conclusion:
- The tin requires more energy to increase the temperature: True
- The gold requires more energy to increase the temperature: False
- They both require the same amount of energy because they have the same mass: False
[tex]\[ Q = m \cdot C \cdot \Delta T \][/tex]
where:
- [tex]\( Q \)[/tex] is the heat energy,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( C \)[/tex] is the specific heat capacity,
- [tex]\( \Delta T \)[/tex] is the change in temperature.
Given the specific values:
- For tin (Sn): [tex]\( C _{ Sn } = 0.240 \frac{ J }{ g \cdot^{\circ} C } \)[/tex]
- For gold (Au): [tex]\( C _{ Au } = 0.129 \frac{ J }{ g \cdot ^{\circ} C } \)[/tex]
- Mass ([tex]\( m \)[/tex]): 25 grams
- Change in temperature ([tex]\( \Delta T \)[/tex]): 10 degrees Celsius
Let's calculate the energy needed for both substances:
### Energy required for tin (Sn):
[tex]\[ Q _{ Sn } = m \cdot C _{ Sn } \cdot \Delta T \][/tex]
[tex]\[ Q _{ Sn } = 25 \, g \cdot 0.240 \, \frac{ J }{ g \cdot ^{\circ} C } \cdot 10 \, ^{\circ} C \][/tex]
[tex]\[ Q _{ Sn } = 25 \cdot 0.240 \cdot 10 \][/tex]
[tex]\[ Q _{ Sn } = 60 \, J \][/tex]
### Energy required for gold (Au):
[tex]\[ Q _{ Au } = m \cdot C _{ Au } \cdot \Delta T \][/tex]
[tex]\[ Q _{ Au } = 25 \, g \cdot 0.129 \, \frac{ J }{ g \cdot ^{\circ} C } \cdot 10 \, ^{\circ} C \][/tex]
[tex]\[ Q _{ Au } = 25 \cdot 0.129 \cdot 10 \][/tex]
[tex]\[ Q _{ Au } = 32.25 \, J \][/tex]
### Comparing the energies:
- Energy required for tin (Sn): 60 J
- Energy required for gold (Au): 32.25 J
From these calculations, we can see that the energy required to raise the temperature of 25 grams of tin by 10 degrees Celsius is 60 J, while the energy required for the same mass and temperature increase of gold is 32.25 J. Therefore, tin requires more energy than gold to achieve the same increase in temperature.
### Conclusion:
- The tin requires more energy to increase the temperature: True
- The gold requires more energy to increase the temperature: False
- They both require the same amount of energy because they have the same mass: False
