An ideal gas undergoes a thermodynamic process in which it exchanges no heat with its surroundings and performs no work. Which of the following correctly identifies the process and the corresponding change in temperature of the gas?

Step-by-step solution

Given that the gas exchanges no heat with the surroundings, q = 0 , which means the process is adiabatic. Since the gas performs no work, w = 0 . This condition is satisfied during free expansion (expansion against zero external pressure). According to the first law of thermodynamics, U = q + w . Substituting the values, we get U = 0 + 0 = 0 . For an ideal gas, the internal energy is a function of temperature only ( U = nC_ v T ). Therefore, U = 0 implies that T = 0 . Thus, the process is an adiabatic free expansio