An ideal gas undergoes isothermal expansion into a vacuum. Which of the following correctly represents the thermodynamic changes for this process?

Step-by-step solution

Expansion into a vacuum is called free expansion. In a vacuum, the external pressure is zero ( P_ ext = 0 ). Work done, w = -P_ ext V = 0 . For an ideal gas undergoing an isothermal process, the change in temperature is zero ( T = 0 ). Since the internal energy of an ideal gas depends only on temperature, the change in internal energy is zero ( U = 0 ). According to the first law of thermodynamics: U = q + w 0 = q + 0 q = 0 Therefore, q = 0 , w = 0 , and U = 0 . Answer: q = 0 , w = 0 , U = 0