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A gas expands isothermally at 300 K from a volume of 1 m³ to 2 m³. If the pressu

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Question: A gas expands isothermally at 300 K from a volume of 1 m³ to 2 m³. If the pressure at the initial state is 100 kPa, what is the work done by the gas?

Options:

  1. 0 kJ
  2. 100 kJ
  3. 150 kJ
  4. 200 kJ

Correct Answer: 100 kJ

Solution: 

Work done (W) = nRT ln(Vf/Vi). Here, nRT = PVi = 100 kPa * 1 m³ = 100 kJ. W = 100 kJ * ln(2) ≈ 69.3 kJ.

A gas expands isothermally at 300 K from a volume of 1 m³ to 2 m³. If the pressu

Practice Questions

Q1
A gas expands isothermally at 300 K from a volume of 1 m³ to 2 m³. If the pressure at the initial state is 100 kPa, what is the work done by the gas?
  1. 0 kJ
  2. 100 kJ
  3. 150 kJ
  4. 200 kJ

Questions & Step-by-Step Solutions

A gas expands isothermally at 300 K from a volume of 1 m³ to 2 m³. If the pressure at the initial state is 100 kPa, what is the work done by the gas?
  • Step 1: Identify the initial volume (Vi) and final volume (Vf) of the gas. Here, Vi = 1 m³ and Vf = 2 m³.
  • Step 2: Note the initial pressure (P) of the gas, which is given as 100 kPa.
  • Step 3: Convert the pressure from kPa to kJ for easier calculations. Since 1 kPa * 1 m³ = 1 kJ, we have PVi = 100 kPa * 1 m³ = 100 kJ.
  • Step 4: Use the formula for work done by the gas during isothermal expansion: W = nRT ln(Vf/Vi).
  • Step 5: Since nRT = PVi, substitute the value we found: W = 100 kJ * ln(2).
  • Step 6: Calculate ln(2), which is approximately 0.693.
  • Step 7: Multiply 100 kJ by 0.693 to find the work done: W ≈ 100 kJ * 0.693 ≈ 69.3 kJ.
  • Isothermal Expansion – The process where a gas expands at a constant temperature, leading to specific calculations for work done.
  • Ideal Gas Law – Understanding the relationship between pressure, volume, and temperature in gases, particularly in isothermal conditions.
  • Natural Logarithm in Work Calculation – Using the natural logarithm to calculate work done during gas expansion, specifically ln(Vf/Vi).
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