2 mol of an ideal gas at 300 K expands isothermally into a vacuum, increasing its volume from 5 L to 10 L . What are the values of work done ( W ) and change in internal energy ( U ) for this process? (Given: R = 8.314 J K ⁻¹ mol ⁻¹ , 2 = 0.693 )

Step-by-step solution

Expansion of a gas into a vacuum is known as free expansion. In a vacuum, the external pressure ( P_ ext ) is zero. The work done against a constant external pressure is given by W = -P_ ext V . Since P_ ext = 0 , the work done W = 0 . For an ideal gas undergoing an isothermal process, the temperature remains constant ( T = 0 ). The internal energy of an ideal gas depends only on temperature, so the change in internal energy U = 0 . Answer: W = 0 , U = 0