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A gas expands in a frictionless piston-cylinder arrangement. The expansion process is very slow, and is resisted by an ambient pressure of 100 kPa. During the expansion process, the pressure of the system (gas) remains constant at 300 kPa. The change in volume of the gas is 0.01 m3. The maximum amount of work that could be utilized from the above process is: 
  • a)
    0 kJ
  • b)
    1 kJ
  • c)
    2 kJ
  • d)
    3 kJ
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A gas expands in a frictionless piston-cylinder arrangement. The expan...
Net pressure action on the piston = 300 KPa - 100 KPa
= 200 KPa
(which is constant throughout the expansion process)
and change in volume = dV = 0.01 m^3
W.D in expansion process = pdv
={200*10^3(N/m^2}x(0.01m^3)
= 2 * 10^3 Nm
= 2 KJ
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Most Upvoted Answer
A gas expands in a frictionless piston-cylinder arrangement. The expan...
The maximum amount of work that could be utilized from the above process is 2 kJ.

Given data:
- Ambient pressure (resistance) = 100 kPa
- Pressure of the system (gas) = 300 kPa
- Change in volume of the gas = 0.01 m3

Calculating work done:
The work done during an expansion process can be calculated using the formula:

W = P * ΔV

Where,
W = work done
P = pressure
ΔV = change in volume

In this case, the pressure of the system remains constant at 300 kPa. Therefore, the work done can be calculated as:

W = 300 kPa * 0.01 m3

Converting units:
To calculate the work done in joules, we need to convert kPa to Pa:

1 kPa = 1000 Pa

Therefore:

W = 300 kPa * 0.01 m3 * 1000 Pa/kPa

Simplifying the equation:

W = 3000 Pa * 0.01 m3

Calculating work done:
W = 30 J

Converting to kilojoules:
To convert joules to kilojoules, we divide by 1000:

W = 30 J / 1000

W = 0.03 kJ

However, since the expansion is resisted by the ambient pressure of 100 kPa, the maximum amount of work that can be utilized is the work done minus the work done against the resistance:

Maximum work utilized = W - P_resistance * ΔV

Substituting the given values:

Maximum work utilized = 0.03 kJ - 100 kPa * 0.01 m3

Converting kPa to Pa:

Maximum work utilized = 0.03 kJ - 1000 Pa * 0.01 m3

Maximum work utilized = 0.03 kJ - 10 J

Maximum work utilized = 2 kJ

Therefore, the maximum amount of work that could be utilized from the above process is 2 kJ (option C).
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Community Answer
A gas expands in a frictionless piston-cylinder arrangement. The expan...
W = Resistance pressure
this is required for atmosphere, means against atmosphere we have to do this. but question is that how much we can use. Now we use a connecting rod so that it can generate 200 KPa pressure extra. so that total resistance pressure is 300 KPa. now total work done = Total Resistance pressure
for atmosphere. 2 KJ for use
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A gas expands in a frictionless piston-cylinder arrangement. The expansion process is very slow, and is resisted by an ambient pressure of 100 kPa. During the expansion process, the pressure of the system (gas) remains constant at 300 kPa. The change in volume of the gas is 0.01 m3. The maximum amount of work that could be utilized from the above process is:a)0 kJb)1 kJc)2 kJd)3 kJCorrect answer is option 'C'. Can you explain this answer?
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