An ideal gas undergoes an isothermal reversible expansion at a constant temperature. The initial pressure of the gas is 5 bar and its initial volume is 10 dm ³ . If the gas absorbs 11.515 kJ of heat from the surroundings during the process, what is the final volume of the gas? (Given: 1 bar dm ³ = 100 J )

Step-by-step solution

For an isothermal process involving an ideal gas, the change in internal energy is zero ( U = 0 ). According to the First Law of Thermodynamics: U = q + w 0 = q + w w = -q Given that the heat absorbed q = +11.515 kJ , the work done by the gas is: w = -11.515 kJ The work done during an isothermal reversible expansion is given by: w = -2.303 P₁ V₁ ₁₀ ( V₂ V₁ ) First, calculate the initial P₁ V₁ product in Joules: P₁ V₁ = 5 bar 10 dm ³ = 50 bar dm ³ Since 1 bar dm ³ = 100 J , we have: P₁ V₁ = 5000 J = 5 kJ Substitute