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Answer :
To find the energy change when the temperature of 13.6 grams of gaseous xenon decreases from 38.5 °C to 22.1 °C, we can use the formula for calculating heat energy change:
[tex]\[ Q = mc\Delta T \][/tex]
where:
- [tex]\( Q \)[/tex] is the heat energy change in joules,
- [tex]\( m \)[/tex] is the mass of the substance in grams,
- [tex]\( c \)[/tex] is the specific heat capacity of the substance (for xenon, this is approximately 0.158 J/g°C),
- [tex]\(\Delta T\)[/tex] is the change in temperature in degrees Celsius.
Let's go through the steps:
1. Identify the given values:
- Mass of xenon, [tex]\( m = 13.6 \)[/tex] grams
- Specific heat capacity of xenon, [tex]\( c = 0.158 \)[/tex] J/g°C
- Initial temperature, [tex]\( T_{\text{initial}} = 38.5 \)[/tex] °C
- Final temperature, [tex]\( T_{\text{final}} = 22.1 \)[/tex] °C
2. Calculate the change in temperature ([tex]\(\Delta T\)[/tex]):
[tex]\[
\Delta T = T_{\text{final}} - T_{\text{initial}} = 22.1 \, °\text{C} - 38.5 \, °\text{C} = -16.4 \, °\text{C}
\][/tex]
3. Calculate the energy change (Q) using the formula:
[tex]\[
Q = mc\Delta T = 13.6 \, \text{g} \times 0.158 \, \frac{\text{J}}{\text{g°C}} \times (-16.4 \, °\text{C})
\][/tex]
4. Compute the result:
[tex]\[
Q = 13.6 \times 0.158 \times (-16.4) = -35.24032 \, \text{Joules}
\][/tex]
The negative sign indicates that energy is released as the temperature of the xenon decreases. Therefore, the energy change is [tex]\(-35.24032\)[/tex] Joules.
[tex]\[ Q = mc\Delta T \][/tex]
where:
- [tex]\( Q \)[/tex] is the heat energy change in joules,
- [tex]\( m \)[/tex] is the mass of the substance in grams,
- [tex]\( c \)[/tex] is the specific heat capacity of the substance (for xenon, this is approximately 0.158 J/g°C),
- [tex]\(\Delta T\)[/tex] is the change in temperature in degrees Celsius.
Let's go through the steps:
1. Identify the given values:
- Mass of xenon, [tex]\( m = 13.6 \)[/tex] grams
- Specific heat capacity of xenon, [tex]\( c = 0.158 \)[/tex] J/g°C
- Initial temperature, [tex]\( T_{\text{initial}} = 38.5 \)[/tex] °C
- Final temperature, [tex]\( T_{\text{final}} = 22.1 \)[/tex] °C
2. Calculate the change in temperature ([tex]\(\Delta T\)[/tex]):
[tex]\[
\Delta T = T_{\text{final}} - T_{\text{initial}} = 22.1 \, °\text{C} - 38.5 \, °\text{C} = -16.4 \, °\text{C}
\][/tex]
3. Calculate the energy change (Q) using the formula:
[tex]\[
Q = mc\Delta T = 13.6 \, \text{g} \times 0.158 \, \frac{\text{J}}{\text{g°C}} \times (-16.4 \, °\text{C})
\][/tex]
4. Compute the result:
[tex]\[
Q = 13.6 \times 0.158 \times (-16.4) = -35.24032 \, \text{Joules}
\][/tex]
The negative sign indicates that energy is released as the temperature of the xenon decreases. Therefore, the energy change is [tex]\(-35.24032\)[/tex] Joules.
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