During an adiabatic process- if the pressure of the ideal gas is proportional to the cube of its temperature- the ratio - -CpCv is Cp- Specific heat at constant pressure - Cv-Specific heat at constant volume

The specific heat at constant pressure and at constant volume for an ideal gas are $C_{p}$ and $C_{v}$ and its adiabatic and isothermal elasticities are $E_{p h i}$ and $E_{θ}$ respectively. The ratio of $E_{ϕ}$ to $E_{θ}$ is

Q. The molar specific heat of an ideal gas at constant pressure and volume are

C_{p}

and

C_{v}

respectively. The value of

C_{v}

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During an adiabatic process, if the pressure of the ideal gas is proportional to the cube of its temperature, the ratio γ=CpCv is(Cp= Specific heat at constant pressure ; Cv=Specific heat at constant volume)

The correct option is C 32Given P∝T3PT−3=constantFor an adiabatic process, we havePTγ1−γ=constantComparing these two equations, we getγ1−γ=−3γ=−3+3γ2γ=3γ=32Option D.

During an adiabatic process, if the pressure of the ideal gas is proportional to the cube of its temperature, the ratio $γ = \frac{C_{p}}{C_{v}}$ is
( $C_{p} =$ Specific heat at constant pressure ; $C_{v} =$ Specific heat at constant volume)

The correct option is C $\frac{3}{2}$
Given $P \propto T^{3}$
$P T^{- 3} =$ constant
For an adiabatic process, we have
$P T^{\frac{γ}{1 - γ}} =$ constant
Comparing these two equations, we get
$\frac{γ}{1 - γ} = - 3$
$γ = - 3 + 3 γ$
$2 γ = 3$
$γ = \frac{3}{2}$
Option D.