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
