Join WhatsApp Icon JEE WhatsApp Group
Question 33

For 1 mol of gas, the plot of pV vs p is shown below. p is the pressure and V is the volume of the gas.

image


What is the value of compressibility factor at point A?

For one mole of a real gas, the Van der Waals equation is

$$\left(P+\frac{a}{V^2}\right)(V-b)=RT.$$

Expanding the equation,

$$PV-Pb+\frac{a}{V}-\frac{ab}{V^2}=RT.$$

Dividing throughout by (RT),

$$\frac{PV}{RT}-\frac{Pb}{RT}+\frac{a}{RTV}-\frac{ab}{RTV^2}=1.$$

Since the compressibility factor is defined as

$$Z=\frac{PV}{RT},$$

we obtain

$$Z-\frac{Pb}{RT}+\frac{a}{RTV}-\frac{ab}{RTV^2}=1.$$

At low pressures, the molar volume (V) is very large, so terms containing (\frac{1}{V^2}) can be neglected. Therefore,

$$Z\approx 1-\frac{a}{RTV}.$$

Point A corresponds to the low-pressure region where intermolecular attractive forces dominate, causing the gas to be more compressible than an ideal gas ((Z<1)). The deviation from ideal behaviour is represented by the attractive term (-\frac{a}{RTV}).

Hence, the compressibility factor at point A is

$$\boxed{Z=1-\frac{a}{RTV}}.$$

Therefore, the correct answer is

$$\boxed{1-\frac{a}{RTV}}.$$

Get AI Help

Create a FREE account and get:

  • Free JEE Mains Previous Papers PDF
  • Take JEE Mains paper tests

JEE Quant Questions | JEE Quantitative Ability

JEE DILR Questions | LRDI Questions For JEE

JEE Verbal Ability Questions | VARC Questions For JEE

Free JEE Topicwise Questions

JEE Rotational MotionJEE Units & MeasurementsJEE Atomic StructureJEE GravitationJEE Periodic Table & PeriodicityJEE StatisticsJEE Inverse Trigonometric FunctionsJEE Magnetism & Magnetic MaterialsJEE Sequences & SeriesJEE MatricesJEE Alternating CurrentsJEE Carboxylic AcidsJEE Permutations & CombinationsJEE Work, Energy & PowerJEE Electromagnetic InductionJEE Electronic DevicesJEE d and f-Block ElementsJEE Chemical KineticsJEE Heat TransferJEE Three Dimensional GeometryJEE Magnetic Effects of CurrentJEE Hydrocarbons - AromaticJEE Electromagnetic WavesJEE Aldehydes & KetonesJEE Hydrocarbons - AlkanesJEE Applications of DerivativesJEE EquilibriumJEE Indefinite IntegrationJEE Chemical ThermodynamicsJEE ElectrochemistryJEE ProbabilityJEE BiomoleculesJEE Continuity & DifferentiabilityJEE Kinetic Theory of GasesJEE Vector AlgebraJEE Hydrocarbons - AlkynesJEE Differential EquationsJEE Current & ResistanceJEE Straight LinesJEE WavesJEE Redox ReactionsJEE Hydrocarbons - AlkenesJEE DeterminantsJEE SolutionsJEE Ray OpticsJEE Dual Nature of Matter & RadiationJEE Chemical Bonding & Molecular StructureJEE Complex NumbersJEE Sets, Relations & FunctionsJEE Electric Charges & FieldsJEE Laws of MotionJEE Fluid MechanicsJEE Basic Concepts in ChemistryJEE Trigonometric FunctionsJEE LimitsJEE Laws of ThermodynamicsJEE Kinematics - 2D MotionJEE p-Block Elements (Groups 13-18)JEE Simple Harmonic MotionJEE Electric Potential & CapacitanceJEE Coordination CompoundsJEE JEE 2D GeometryJEE CirclesJEE Definite IntegrationJEE EMF & Circuit AnalysisJEE Surface TensionJEE Atoms & NucleiJEE Laboratory Experiments - XIJEE Number SystemJEE Basic Principles of Organic ChemistryJEE Wave OpticsJEE Quadratic EquationsJEE Alcohols, Phenols & EthersJEE Organic Compounds with HalogensJEE DifferentiationJEE Conic SectionsJEE Nitrogen-Containing CompoundsJEE ElasticityJEE Practical Organic ChemistryJEE Kinematics - 1D MotionJEE Purification & CharacterisationJEE Binomial Theorem
Ask AI