Consider the adiabatic free expansion of an ideal gas. Read the following statements: (I) The work done by the gas is zero. (II) The temperature of the gas decreases during the process. (III) The change in internal energy of the gas is zero. (IV) The process is thermodynamically reversible. How many of the given statements are correct?

Step-by-step solution

For free expansion, the gas expands against a vacuum, meaning the external pressure is zero ( P_ ext = 0 ). Therefore, the work done is w = -P_ ext V = 0 . Statement (I) is correct. Since the process is adiabatic, the heat exchange is zero ( q = 0 ). According to the first law of thermodynamics, U = q + w . Substituting the values gives U = 0 + 0 = 0 . Statement (III) is correct. For an ideal gas, the internal energy depends only on temperature. Since U = 0 , the change in temperature T = 0 . The temperature remain