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JEE Main 20245 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
5 April
Shift
Evening Shift
Subject
Physics
Chapter
Kinetic Theory of Gases

JEE Main 2024 · 5 April · Evening Shift · Physics · Kinetic Theory of Gases

During an adiabatic process, if the pressure of a gas is found to...

During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of CPCV\frac{C_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}} for the gas is :

Options

  1. A53\frac{5}{3}
  2. B97\frac{9}{7}
  3. C32\frac{3}{2}
  4. D75\frac{7}{5}

Correct answer

C. 32\frac{3}{2}

Step-by-step solution

P∝T3PT−3= constant ∵PVT=nR= constant from ideal gas equation (P)(PV)−3= constant P−2V−3= cosntant ...(i)\begin{aligned} & \mathrm{P} \propto \mathrm{T}^3 \\ & \mathrm{PT}^{-3}=\text{ constant } \\ & \because \frac{\mathrm{PV}}{\mathrm{T}}=\mathrm{nR}=\text{ constant from ideal gas equation } \\ & (\mathrm{P})(\mathrm{PV})^{-3}=\text{ constant } \\ & \mathrm{P}^{-2} \mathrm{ V}^{-3}=\text{ cosntant }...(i) \end{aligned}\becauseProcessequationforadiabaticprocessisProcess equation for adiabatic process is\mathrm{PV}^{\mathrm{y}}=\text{ constant }...(ii)Comparingequation(1)and(2)Comparing equation (1) and (2)\frac{C_P}{C_V}=y=\frac{3}{2}$
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