Question:
1 mole of rigid diatomic gas performs a work of $\mathrm{Q} / 5$ when heat $\mathrm{Q}$ is supplied to it. The molar heat capacity of the gas during this
transformation is $\frac{x R}{8}$, The value of $x$ is
$[\mathrm{K}=$ universal gas constant $]$
Solution:
$\mathrm{Q}=\Delta \mathrm{U}+\mathrm{W}$
$\mathrm{Q}=\Delta \mathrm{U}+\frac{\mathrm{Q}}{5}$
$\Delta U=\frac{4 Q}{5}$
$\mathrm{nC}_{\mathrm{v}} \Delta \mathrm{T}=\frac{4}{5} \mathrm{nC} \Delta \mathrm{T}$
$\frac{5}{4} C_{V}=C$
$\mathrm{C}=\frac{5}{4}\left(\frac{\mathrm{f}}{2}\right) \mathrm{R}=\frac{5}{4}\left(\frac{5}{2}\right) \mathrm{R}$
$C=\frac{25}{8} R$
$x=25$
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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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