Two ideal polyatomic gases at temperatures $T_{1}$ and $T_{2}$ are mixed so that there is no loss of energy. If $F_{1}$ and $F_{2}, m_{1}$ and $m_{2}, n_{1}$ and $n_{2}$ be the degrees of freedom, masses, number of molecules of the first and second gas respectively, the temperature of mixture of these two gases is :
$\frac{\mathrm{n}_{1} \mathrm{~T}_{1}+\mathrm{n}_{2} \mathrm{~T}_{2}}{\mathrm{n}_{1}+\mathrm{n}_{2}}$
$\frac{\mathrm{n}_{1} \mathrm{~F}_{1} \mathrm{~T}_{1}+\mathrm{n}_{2} \mathrm{~F}_{2} \mathrm{~T}_{2}}{\mathrm{n}_{1} \mathrm{~F}_{1}+\mathrm{n}_{2} \mathrm{~F}_{2}}$
$\frac{\mathrm{n}_{1} \mathrm{~F}_{1} \mathrm{~T}_{1}+\mathrm{n}_{2} \mathrm{~F}_{2} \mathrm{~T}_{2}}{\mathrm{~F}_{1}+\mathrm{F}_{2}}$
$\frac{\mathrm{n}_{1} \mathrm{~F}_{1} \mathrm{~T}_{1}+\mathrm{n}_{2} \mathrm{~F}_{2} \mathrm{~T}_{2}}{\mathrm{n}_{1}+\mathrm{n}_{2}}$
Correct Option: , 2
Let the final temperature of the mixture be $\mathrm{T}$.
Since, there is no loss in energy.
$\Delta \mathrm{U}=0$
$\Rightarrow \frac{\mathrm{F}_{1}}{2} \mathrm{n}_{1} \mathrm{R} \Delta \mathrm{T}+\frac{\mathrm{F}_{2}}{2} \mathrm{n}_{2} \mathrm{R} \Delta \mathrm{T}=0$
$\Rightarrow \frac{\mathrm{F}_{1}}{2} \mathrm{n}_{1} \mathrm{R}\left(\mathrm{T}_{1}-\mathrm{T}\right)+\frac{\mathrm{F}_{2}}{2} \mathrm{n}_{2} \mathrm{R}\left(\mathrm{T}_{2}-\mathrm{T}\right)=0$
$\Rightarrow \mathrm{T}=\frac{\mathrm{F}_{1} \mathrm{n}_{1} \mathrm{RT}_{1}+\mathrm{F}_{2} \mathrm{n}_{2} \mathrm{RT} \mathrm{T}_{2}}{\mathrm{~F}_{1} \mathrm{n}_{1} \mathrm{R}+\mathrm{F}_{2} \mathrm{n}_{2} \mathrm{R}} \Rightarrow \frac{\mathrm{F}_{1} \mathrm{n}_{1} \mathrm{~T}_{1}+\mathrm{F}_{2} \mathrm{n}_{2} \mathrm{~T}_{2}}{\mathrm{~F}_{1} \mathrm{n}_{1}+\mathrm{F}_{2} \mathrm{n}_{2}}$
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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,