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Answer :
To find out how much energy is released when 38.4 grams of lignin benzene is cooled from 93.0°C to 15.0°C, we can use the formula for calculating the heat energy (Q) released:
[tex]\[ Q = m \times Cs \times \Delta T \][/tex]
Where:
- [tex]\( Q \)[/tex] is the heat energy released (in Joules).
- [tex]\( m \)[/tex] is the mass of the substance (in grams).
- [tex]\( Cs \)[/tex] is the specific heat capacity (in J/g°C).
- [tex]\( \Delta T \)[/tex] is the change in temperature (in °C).
### Steps:
1. Identify the given values:
- Mass ([tex]\( m \)[/tex]) = 38.4 grams
- Specific heat capacity ([tex]\( Cs \)[/tex]) = 1.73 J/g°C
- Initial temperature = 93.0°C
- Final temperature = 15.0°C
2. Calculate the change in temperature ([tex]\( \Delta T \)[/tex]):
[tex]\[
\Delta T = \text{Final Temperature} - \text{Initial Temperature} = 15.0°C - 93.0°C = -78.0°C
\][/tex]
3. Substitute the values into the formula:
[tex]\[
Q = 38.4 \, \text{g} \times 1.73 \, \text{J/g°C} \times (-78.0°C)
\][/tex]
4. Calculate the energy released:
[tex]\[
Q = -5181.696 \, \text{J}
\][/tex]
This negative sign indicates that energy is released during the process. Therefore, the energy released when cooling 38.4 grams of lignin benzene from 93.0°C to 15.0°C is 5181.696 Joules.
[tex]\[ Q = m \times Cs \times \Delta T \][/tex]
Where:
- [tex]\( Q \)[/tex] is the heat energy released (in Joules).
- [tex]\( m \)[/tex] is the mass of the substance (in grams).
- [tex]\( Cs \)[/tex] is the specific heat capacity (in J/g°C).
- [tex]\( \Delta T \)[/tex] is the change in temperature (in °C).
### Steps:
1. Identify the given values:
- Mass ([tex]\( m \)[/tex]) = 38.4 grams
- Specific heat capacity ([tex]\( Cs \)[/tex]) = 1.73 J/g°C
- Initial temperature = 93.0°C
- Final temperature = 15.0°C
2. Calculate the change in temperature ([tex]\( \Delta T \)[/tex]):
[tex]\[
\Delta T = \text{Final Temperature} - \text{Initial Temperature} = 15.0°C - 93.0°C = -78.0°C
\][/tex]
3. Substitute the values into the formula:
[tex]\[
Q = 38.4 \, \text{g} \times 1.73 \, \text{J/g°C} \times (-78.0°C)
\][/tex]
4. Calculate the energy released:
[tex]\[
Q = -5181.696 \, \text{J}
\][/tex]
This negative sign indicates that energy is released during the process. Therefore, the energy released when cooling 38.4 grams of lignin benzene from 93.0°C to 15.0°C is 5181.696 Joules.
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