Answer :
To determine how much work is done by the gas as it expands, you can use the formula for work done by a gas during expansion or contraction:
[tex]\[ \text{Work} = - P_{\text{external}} \times \Delta V \][/tex]
where:
- [tex]\( P_{\text{external}} \)[/tex] is the external pressure (in atmospheres, atm).
- [tex]\( \Delta V \)[/tex] is the change in volume (final volume minus initial volume, in liters).
Let's break down the steps:
1. Identify the initial and final volumes:
- Initial Volume ([tex]\( V_{\text{initial}} \)[/tex]) = 4.00 L
- Final Volume ([tex]\( V_{\text{final}} \)[/tex]) = 8.00 L
2. Calculate the change in volume ([tex]\( \Delta V \)[/tex]):
[tex]\[ \Delta V = V_{\text{final}} - V_{\text{initial}} = 8.00\, \text{L} - 4.00\, \text{L} = 4.00\, \text{L} \][/tex]
3. Identify the external pressure:
- External Pressure ([tex]\( P_{\text{external}} \)[/tex]) = 1.22 atm
4. Calculate the work done:
[tex]\[ \text{Work} = - P_{\text{external}} \times \Delta V = - 1.22\, \text{atm} \times 4.00\, \text{L} \][/tex]
5. Perform the multiplication:
[tex]\[ \text{Work} = - 4.88\, \text{L}\cdot\text{atm} \][/tex]
The work done by the gas is [tex]\(-4.88\, \text{L}\cdot\text{atm}\)[/tex]. The negative sign indicates that the work is done by the system (the gas) on the surroundings during expansion.
[tex]\[ \text{Work} = - P_{\text{external}} \times \Delta V \][/tex]
where:
- [tex]\( P_{\text{external}} \)[/tex] is the external pressure (in atmospheres, atm).
- [tex]\( \Delta V \)[/tex] is the change in volume (final volume minus initial volume, in liters).
Let's break down the steps:
1. Identify the initial and final volumes:
- Initial Volume ([tex]\( V_{\text{initial}} \)[/tex]) = 4.00 L
- Final Volume ([tex]\( V_{\text{final}} \)[/tex]) = 8.00 L
2. Calculate the change in volume ([tex]\( \Delta V \)[/tex]):
[tex]\[ \Delta V = V_{\text{final}} - V_{\text{initial}} = 8.00\, \text{L} - 4.00\, \text{L} = 4.00\, \text{L} \][/tex]
3. Identify the external pressure:
- External Pressure ([tex]\( P_{\text{external}} \)[/tex]) = 1.22 atm
4. Calculate the work done:
[tex]\[ \text{Work} = - P_{\text{external}} \times \Delta V = - 1.22\, \text{atm} \times 4.00\, \text{L} \][/tex]
5. Perform the multiplication:
[tex]\[ \text{Work} = - 4.88\, \text{L}\cdot\text{atm} \][/tex]
The work done by the gas is [tex]\(-4.88\, \text{L}\cdot\text{atm}\)[/tex]. The negative sign indicates that the work is done by the system (the gas) on the surroundings during expansion.
