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Five moles of an ideal gas at 27° C are allowed to expand isothermally from an initial pressure of 10.0 atm to a final pressure of 4.0 atm against a constant external pressure of 1.0 atm. Thus, work done will be
  • a)
    - 1870.6 J
  • b)
    - 1870.6J
  • c)
    -18.47 J
  • d)
    +18.47 J
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Five moles of an ideal gas at 27° C are allowed to expand isother...
Work done during isothermal irreversible process is given by the formula w = -pext (nrt/p2-nrt/p1)
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Most Upvoted Answer
Five moles of an ideal gas at 27° C are allowed to expand isother...
Understanding the Problem
To calculate the work done by the gas during isothermal expansion, we can use the formula for work done in a gas expansion against a constant external pressure.
Given Data
- Moles of gas (n): 5 moles
- Initial pressure (P1): 10.0 atm
- Final pressure (P2): 4.0 atm
- External pressure (Pext): 1.0 atm
- Temperature (T): 27°C (or 300 K)
Work Done Calculation
The work done (W) by the gas during expansion against a constant external pressure is given by the formula:
W = -Pext * ΔV
Where ΔV is the change in volume. Since the process is isothermal, we can relate the pressures and volumes using the ideal gas law:
- Initial volume (V1) can be calculated as:
V1 = (nRT) / P1
- Final volume (V2) can be calculated as:
V2 = (nRT) / P2
Thus, the change in volume (ΔV) is:
ΔV = V2 - V1
Substituting the values and solving for the volumes:
- V1 = (5 moles * 0.0821 L·atm/K·mol * 300 K) / 10 atm = 12.315 L
- V2 = (5 moles * 0.0821 L·atm/K·mol * 300 K) / 4 atm = 30.7875 L
Now, the change in volume (ΔV) is:
ΔV = 30.7875 L - 12.315 L = 18.4725 L
Now, converting liters to cubic meters (1 L = 0.001 m³), we have:
ΔV = 0.0184725 m³
Now, substituting into the work done formula:
W = -Pext * ΔV = -1 atm * 0.0184725 m³ = -1 * 101.325 J/atm * 0.0184725 m³ = -1870.6 J
Thus, the work done by the gas is -1870.6 J, indicating work done by the system (expansion).
Conclusion
The correct answer is option 'A': 1870.6 J (work done by the gas).
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Community Answer
Five moles of an ideal gas at 27° C are allowed to expand isother...
-1870.6J
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Five moles of an ideal gas at 27° C are allowed to expand isothermally from an initial pressure of 10.0 atm to a final pressure of 4.0 atm against a constant external pressure of 1.0 atm. Thus, work done will bea)- 1870.6 Jb)- 1870.6Jc)-18.47 Jd)+18.47 JCorrect answer is option 'A'. Can you explain this answer?
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