Two moles of an ideal gas at 300 ~K expand isothermally into an evacuated vessel (vacuum) until its volume doubles. Which of the following sets of values is correct for this process? (Given: 2 = 0.693 , R = 8.314 ~J ~K ⁻¹ ~mol ⁻¹ )

Step-by-step solution

Expansion into an evacuated vessel (vacuum) is called free expansion. In this case, the external pressure ( P_ ext ) is zero. Work done, w = -P_ ext V = 0 . Since the process is isothermal and involves an ideal gas, the change in temperature ( T ) is zero. The internal energy of an ideal gas depends only on temperature, so U = 0 . According to the first law of thermodynamics, U = q + w . Substituting the values gives 0 = q + 0 , which means q = 0 . Therefore, w = 0 , q = 0 , and U = 0 . Answer: w = 0, q = 0, U = 0