In a typical combustion engine the work don
by a gas molecule is given $W=\alpha^{2} \beta e^{\frac{-\beta x^{2}}{k T}}$
where $x$ is the displacement, $k$ is the Boltzmann constant and $\mathrm{T}$ is the temperature. If $\alpha$ and $\beta$ are constants, dimensions of $\alpha$ will be :
$\left[\mathrm{MLT}^{-2}\right]$
$\left[\mathrm{M}^{0} \mathrm{LT}^{0}\right]$
$\left[\mathrm{M}^{2} \mathrm{LT}^{-2}\right]$
$\left[\mathrm{MLT}^{-1}\right]$
Correct Option: , 2
kT has dimension of energy
$\frac{\beta x^{2}}{k T}$ is dimensionless
${[\beta]\left[\mathrm{L}^{2}\right]=\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right] }$
${[\beta]=\left[\mathrm{MT}^{-2}\right] }$
$\alpha^{2} \beta$ has dimensions of work
${\left[\alpha^{2}\right]\left[\mathrm{MT}^{-2}\right]=\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right] }$
${[\alpha]=\left[\mathrm{M}^{0} \mathrm{LT}^{0}\right] }$
Ans. 2
- JEE Main
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- Motion in a Plane
- Law of Motion
- Work, Energy and Power
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- Oscillations
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- 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
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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,