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    Real gas behavior approaches ideal gas equation when
    Question

    Real gas behavior approaches ideal gas equation when

    A.

    Pressure and temperature are very high

    B.

    Pressure is very high and temperature is very low

    C.

    Pressure and temperature are very low

    D.

    Pressure is very low and temperature is very high

    Correct option is D

    Ideal Gas Law:PV=nRTAssumes:- Zero molecular volume.- No intermolecular forces.Real gases deviate due to:- Finite molecular size (excluded volume)- Intermolecular forces (e.g., van der Waals)Mathematical Justification (van der Waals Equation):(P+an2V2)(Vnb)=nRTAs P0 and T:an2V20(forces negligible)VnbV(volume correction negligible)Reduces to PV=nRT\textbf{Ideal Gas Law:} \quad PV = nRT\text{Assumes:} \\\text{- Zero molecular volume.} \\\text{- No intermolecular forces.} \\\text{Real gases deviate due to:} \\\textbf{- Finite molecular size} \ (\text{excluded volume}) \\\textbf{- Intermolecular forces} \ (\text{e.g., van der Waals})\\[1em]\textbf{Mathematical Justification (van der Waals Equation):} \\\left( P + \frac{an^2}{V^2} \right)(V - nb) = nRT\\[1em]\text{As } P \to 0 \text{ and } T \to \infty: \\\quad \frac{an^2}{V^2} \to 0 \quad \text{(forces negligible)} \\\quad V - nb \approx V \quad \text{(volume correction negligible)} \\\quad \text{Reduces to } PV = nRT​​

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