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JIPMER 2014
Exam
JIPMER
Year
2014
Subject
Physics
Chapter
Thermodynamics

JIPMER 2014 · Physics · Thermodynamics

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

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of absolute temperature. The ratio CpCV\frac{C_p}{C_V} for the gas is

Options

  1. A43\frac{4}{3}
  2. B22
  3. C53\frac{5}{3}
  4. D32\frac{3}{2}

Correct answer

D. 32\frac{3}{2}

Step-by-step solution

Given, that p∝T3p \propto T^3 or pT−3= constant …(i)p T^{-3}=\text{ constant } \quad \ldots(i) Also for adiabatic process, pVγ= constant \mathrm{pV}^\gamma=\text{ constant } But pV=RTp V=R T (ideal gas law) or V=RTpV=\frac{R T}{p}∴p(RTp)γ= constant p1−γTγ= constant \begin{aligned} \therefore \quad p\left(\frac{R T}{p}\right)^\gamma & =\text{ constant } \\ p^{1-\gamma} T^\gamma & =\text{ constant }\end{aligned} or pTγ/(1−γ)= constant …(ii)\text{ or } \quad p T^{\gamma /(1-\gamma)}=\text{ constant } \quad \ldots(ii) Equating Eqs. (i) and (ii), we get γ1−γ=−3orγ=−3+3γor2γ=3∴γ=32CpCV=32\frac{\gamma}{1-\gamma}=-3 or \gamma=-3+3 \gamma or 2 \gamma=3\therefore \gamma=\frac{3}{2}\frac{C_p}{C_V}=\frac{3}{2}
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