Thermodynamics

Statement I
During isothermal expansion of an ideal gas its enthalpy decreases.
For an ideal gas, enthalpyH=U+pV.
For an ideal gas:
U=nCVT
and since internal energyUdepends only on temperature for an ideal gas,
dU=0‌‌if temperature is constant (isothermal process).
Also,pV=nRT.
Therefore,
H=U+pV=nCVT+nRT=n(CV+R)T=nCPT
SinceTis constant (isothermal), enthalpyHis also constant.
Hence, enthalpy does not decrease, it remains the same.
Statement I is incorrect.

Statement II
When 2.0 L of an ideal gas expands isothermally into vacuum,∆U=0.
For free expansion into vacuum:
External pressure=0
Sow=0
No heat exchange (q=0) because the system is isolated (expanding into vacuum)
Thus,∆U=q+w=0+0=0
Also, for an ideal gas,∆Udepends only on temperature, and since it is isothermal, ∆U=0.
Statement II is correct.
Final Answer
Statement I is not correct but Statement II is correct.
Correct option: D