The entropy of any system is given by
$S=\alpha^{2} \beta \ln \left[\frac{\mu \mathrm{kR}}{\mathrm{J} \beta^{2}}+3\right]$
where $\alpha$ and $\beta$ are the constants. $\mu, J, k$ and $R$ are no. of moles, mechanical equivalent of heat, Boltzmann constant and gas constant respectively.
$\left[\operatorname{Take} S=\frac{\mathrm{dQ}}{\mathrm{T}}\right]$
Choose the incorrect option from the following :
$\alpha$ and $J$ have the same dimensions.
$\mathrm{S}, \beta, \mathrm{k}$ and $\mu \mathrm{R}$ have the same dimensions.
$\mathrm{S}$ and $\alpha$ have different dimensions.
$\alpha$ and $k$ have the same dimensions.
Correct Option: , 4
$\mathrm{S}=\alpha^{2} \beta \ln \left(\frac{\mu \mathrm{KR}}{\mathrm{J} \beta^{2}}+3\right)$
$\mathrm{S}=\frac{\mathrm{Q}}{\mathrm{T}}=$ joulek $/ \mathrm{k}$
$\left[\alpha^{2} \beta\right]=$ Joule $/ \mathrm{k}$
$\mathrm{PV}=\mathrm{nRT} \quad\left[\frac{\mu \mathrm{KR}}{\mathrm{J} \beta^{2}}\right]=1$
$R=\frac{\text { Joule }}{K}$
$\Rightarrow \mathrm{R}=\frac{\text { Joule }}{\mathrm{K}}, \mathrm{K}=\frac{\text { Joule }}{\mathrm{R}}$
$\Rightarrow \beta=\left(\frac{\text { Joule }}{K}\right)$
$\alpha^{2} \beta=\left(\frac{\text { Joule }}{\mathrm{K}}\right)$
$\Rightarrow \alpha=$ dimensionless
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,