A ideal gas is allowed to extend from 1 L to 10 L against a constant external pressure of 1 bar. The work done in kJ is
Answer (1)
28th Mar, 2025
To calculate the work done when an ideal gas expands against a constant external pressure, we can use the formula for work done in an isobaric process:
W=−PextΔVW = - P_{\text{ext}} \Delta V
Where:
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W is the work done by the gas.
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Pext is the external pressure (in this case, 1 bar).
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ΔV\Delta V is the change in volume (final volume - initial volume).
Step 1: Convert units
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The external pressure Pext is given as 1 bar, but we need it in pascals (Pa) for standard SI units.
1 bar=105Pa -
The volume change ΔV\Delta V is given in liters. We need to convert it to cubic meters (m³):
Step 2: Calculate the work
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Initial volume Vi=1L=1×10−3m3
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Final volume Vf=10L=10×10−3m3
- The change in volume ΔV=Vf−Vi=10×10−3−1×10−3=9×10−3m3
- Now, plug the values into the work formula:
- W= −(1×105Pa) ×(9×10−3m3)
- W=−900Pa⋅m3
- Since 1 Pa⋅m3=1J, the work is:
- W=−900J=−0.9kJ
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Final Answer:
The work done by the gas is −0.9kJ.
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