Question:
An ideal gas is expanding such that $\mathrm{PT}^{3}=$ constant. The coefficient of volume expansion of the gas is:
$\frac{1}{T}$
$\frac{2}{\mathrm{~T}}$
$\frac{4}{T}$
$\frac{3}{\mathrm{~T}}$
Correct Option: , 3
Solution:
$\mathrm{PT}^{3}=\mathrm{constant}$
$\left(\frac{\mathrm{nRT}}{\mathrm{V}}\right) \mathrm{T}^{3}=\mathrm{constant}$
$\mathrm{T}^{4} \mathrm{~V}^{-1}=\mathrm{constant}$
$\mathrm{T}^{4}=\mathrm{kV}$
$\Rightarrow 4 \frac{\Delta \mathrm{T}}{\mathrm{T}}=\frac{\Delta \mathrm{V}}{\mathrm{V}}$...(1)
$\Delta \mathrm{V}=\mathrm{V} \gamma \Delta \mathrm{T}$...(2)
comparing (1) and (2)
we get
$\gamma=\frac{4}{\mathrm{~T}}$
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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,
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