$\mathrm{n}$ mole a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes.
$\mathrm{A} \rightarrow \mathrm{B}:$ Isothermal expansion at temperature $T$ so that the volume is doubled from $V_{1}$ to $V_{2}=2 V_{1}$ and pressure changes from $P_{1}$ to $P_{2}$.
$\mathrm{B} \rightarrow \mathrm{C}:$ Isobaric compression at pressure $\mathrm{P}_{2}$ to initial volume $V_{1}$.
$\mathrm{C} \rightarrow \mathrm{A}:$ Isochoric change leading to change of pressure from $P_{2}$ to $P_{1}$.
Total workdone in the complete cycle ABCA is :
0
$\mathrm{nRT}\left(\ln 2+\frac{1}{2}\right)$
$\mathrm{nRT} \ln 2$
$\mathrm{nRT}\left(\ln 2-\frac{1}{2}\right)$
Correct Option: , 4
$\mathrm{W}_{\text {Isothermal }}=\mathrm{nRTln}\left(\frac{\mathrm{v}_{2}}{\mathrm{v}_{1}}\right)$
$\mathrm{W}_{\text {Isobaric }}=\mathrm{P} \Delta \mathrm{V}=\mathrm{nR} \Delta \mathrm{T}$
$\mathrm{W}_{\text {Isochoric }}=0$
$\mathrm{W}_{1}=\mathrm{nRT} \ln \left(\frac{2 \mathrm{~V}}{\mathrm{~V}}\right)=\mathrm{nRT} \ln 2$
$\mathrm{W}_{2}=\mathrm{nR}\left(\frac{\mathrm{T}}{2}-\mathrm{T}\right)=-\mathrm{nR} \frac{\mathrm{T}}{2}$
$\mathrm{W}_{3}=0$
$\Rightarrow \mathrm{W}_{\text {net }}=\mathrm{W}_{1}+\mathrm{W}_{2}+\mathrm{W}_{3}$
$\mathrm{W}_{\mathrm{net}}=\mathrm{nRT}\left(\ln 2-\frac{1}{2}\right)$
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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,