An ideal gas undergoes an expansion from volume V₁ to V₂ ( V₂ > V₁ ). During this process, it is observed that the heat exchange with the surroundings is zero ( q = 0 ) and the change in temperature of the gas is also zero ( T = 0 ). Under which of the following conditions did this expansion occur?

Step-by-step solution

For an ideal gas, the change in internal energy ( U ) depends only on the change in temperature ( T ). Since it is given that T = 0 , it follows that U = 0 . The problem also states that the heat exchange q = 0 . Applying the first law of thermodynamics, U = q + w . Substituting the known values gives 0 = 0 + w , which means the work done w = 0 . The work done during expansion is given by w = -P_ ext V . Since the gas undergoes expansion ( V₂ > V₁ , so V > 0 ) and w = 0 , the external pressure P_ ext must be zero.