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Nitrogen gas (molecular weight 28) is enclosed in a cylinder by a piston, at the initial condition of 2 bar, 298 K and 1 m3. In a particular process, the gas slowly expands under isothermal condition, until the volume becomes 2m3. Heat exchange occurs with the atmosphere at 298 K during this process.
Q.
The work interaction for the Nitrogen gas is:
  • a)
    200 kJ
  • b)
    138.6 kJ
  • c)
    2 kJ
  • d)
    –200 kJ
Correct answer is option 'B'. Can you explain this answer?
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Given data:
Initial pressure (P1) = 2 bar
Initial volume (V1) = 1 m^3
Final volume (V2) = 2 m^3
Atmospheric temperature (T) = 298 K
Molecular weight of nitrogen gas (M) = 28

The work interaction for the nitrogen gas can be calculated using the formula:
W = -P * ΔV

To calculate the work interaction, we need to find the change in volume (ΔV) and the pressure (P) at each stage.

Step 1: Finding the final pressure (P2)
Since the process is isothermal, the temperature remains constant at 298 K. According to the ideal gas law, we can use the following equation:
P1 * V1 = P2 * V2

Substituting the given values:
2 * 1 = P2 * 2
P2 = 1 bar

Step 2: Finding the change in volume (ΔV)
ΔV = V2 - V1
ΔV = 2 m^3 - 1 m^3
ΔV = 1 m^3

Step 3: Calculating the work interaction
W = -P * ΔV
W = -(P2 - P1) * ΔV
W = -(1 bar - 2 bar) * 1 m^3
W = -(-1 bar) * 1 m^3
W = 1 bar * 1 m^3

Converting the pressure from bar to Pascal:
1 bar = 100,000 Pa
W = 1 * 100,000 * 1
W = 100,000 J

Since the work is given in joules, we need to convert it to kilojoules:
1 kJ = 1000 J
W = 100,000 J / 1000
W = 100 kJ

Therefore, the work interaction for the nitrogen gas is 100 kJ.

The correct answer is not listed among the given options.
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Nitrogen gas (molecular weight 28) is enclosed in a cylinder by a piston, at the initial condition of 2 bar, 298 K and 1 m3. In a particular process, the gas slowly expands under isothermal condition, until the volume becomes 2m3. Heat exchange occurs with the atmosphere at 298 K during this process.Q.The work interaction for the Nitrogen gas is:a)200 kJb)138.6 kJc)2 kJd)–200 kJCorrect answer is option 'B'. Can you explain this answer?
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