NEETChemistryThermodynamics (C)
One mole of an ideal gas is allowed to expand freely into an evacuated and thermally insulated vessel. What are the values of the change in internal energy ( U ) and the change in enthalpy ( H ) for this process?
Options
- AU < 0 , H < 0
- BU = 0 , H = 0
- CU = 0 , H > 0
- DU > 0 , H = 0
Correct answer
B. U = 0 , H = 0
Step-by-step solution
The vessel is thermally insulated, which means no heat is exchanged with the surroundings, so q = 0 . The gas expands freely into an evacuated vessel, meaning the external pressure is zero ( P_ ext = 0 ). Therefore, the work done is w = -P_ ext V = 0 . From the first law of thermodynamics, the change in internal energy is U = q + w = 0 + 0 = 0 . For an ideal gas, the change in enthalpy is given by H = U + (PV) = U + nR T . Since U = 0 for an ideal gas, the change in temperature T = 0 . Substituting these values giv