Question

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio $C_p/C_v$ for the gas is

• A. 4/3
• B. 2
• C. 5/3
• D. 3/2

Answer 1

Answer: (D)

Given that, $p\propto T^3$
or $p{T}^{-3}=$ constant .....(i)
Also for adiabatic process
$p{V}^{{\rm Y}}=$ constant
but $pV=RT$ (ideal gas law)
or $V=\frac{RT}{p}$
$=p{\left(\frac{RT}{p}\right)}^{{\rm Y}}=$ constant
$\Rightarrow p^{1-{\rm Y}}{T}^{{\rm Y}}=$ constant
or $p{T}^{{\rm Y}/(1-{\rm Y})}=$ constant
Equating Eqs. (i) and (ii), we get
$\frac{{\rm Y}}{1-{\rm Y}}=-3$
or ${\rm Y}=-3+3{\rm Y}$
or $2\gamma =3$
$\therefore ={\rm Y}=3/2$
or $\frac{C_p}{C_v}=3/2$