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Answer :
Sure! Let's find out the energy change involved when the temperature of 11.6 grams of gaseous oxygen is decreased from 37.6 °C to 24.4 °C.
Here's how you can solve it:
1. Identify what's given:
- Mass of gaseous oxygen: 11.6 grams
- Initial temperature: 37.6 °C
- Final temperature: 24.4 °C
- Specific heat capacity of gaseous oxygen: 0.918 J/(g°C)
2. Calculate the change in temperature (ΔT):
- ΔT = Final temperature - Initial temperature
- ΔT = 24.4 °C - 37.6 °C
- ΔT = -13.2 °C
The negative sign shows that the temperature is decreasing.
3. Use the formula for energy change:
The formula to calculate the energy change when the temperature changes is:
[tex]\[ Q = m \times c \times \Delta T \][/tex]
Where:
- [tex]\( Q \)[/tex] is the energy change in Joules,
- [tex]\( m \)[/tex] is the mass in grams,
- [tex]\( c \)[/tex] is the specific heat capacity in J/(g°C),
- [tex]\( \Delta T \)[/tex] is the change in temperature in °C.
4. Substitute the values into the formula:
- [tex]\( m = 11.6 \)[/tex] grams
- [tex]\( c = 0.918 \)[/tex] J/(g°C)
- [tex]\( \Delta T = -13.2 \)[/tex] °C
[tex]\[ Q = 11.6 \times 0.918 \times (-13.2) \][/tex]
5. Calculate the energy change:
- [tex]\( Q = 11.6 \times 0.918 \times (-13.2) \)[/tex]
- [tex]\( Q = -140.56416 \)[/tex] Joules
So, the energy change is approximately [tex]\(-140.56\)[/tex] Joules. The negative sign indicates that the system is losing energy as the temperature is decreasing.
Here's how you can solve it:
1. Identify what's given:
- Mass of gaseous oxygen: 11.6 grams
- Initial temperature: 37.6 °C
- Final temperature: 24.4 °C
- Specific heat capacity of gaseous oxygen: 0.918 J/(g°C)
2. Calculate the change in temperature (ΔT):
- ΔT = Final temperature - Initial temperature
- ΔT = 24.4 °C - 37.6 °C
- ΔT = -13.2 °C
The negative sign shows that the temperature is decreasing.
3. Use the formula for energy change:
The formula to calculate the energy change when the temperature changes is:
[tex]\[ Q = m \times c \times \Delta T \][/tex]
Where:
- [tex]\( Q \)[/tex] is the energy change in Joules,
- [tex]\( m \)[/tex] is the mass in grams,
- [tex]\( c \)[/tex] is the specific heat capacity in J/(g°C),
- [tex]\( \Delta T \)[/tex] is the change in temperature in °C.
4. Substitute the values into the formula:
- [tex]\( m = 11.6 \)[/tex] grams
- [tex]\( c = 0.918 \)[/tex] J/(g°C)
- [tex]\( \Delta T = -13.2 \)[/tex] °C
[tex]\[ Q = 11.6 \times 0.918 \times (-13.2) \][/tex]
5. Calculate the energy change:
- [tex]\( Q = 11.6 \times 0.918 \times (-13.2) \)[/tex]
- [tex]\( Q = -140.56416 \)[/tex] Joules
So, the energy change is approximately [tex]\(-140.56\)[/tex] Joules. The negative sign indicates that the system is losing energy as the temperature is decreasing.
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