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

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?

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).