Question

Figure, shows two adiabatic curves for two gases, helium and carbon dioxide. Which curve corresponds to helium?

• A. $A$
• B. $B$
• C. both $\left(A\right)$ and $\left(B\right)$
• D. Can't be predicted.

Answer 1

The correct option is B $B$

The adiabatic process is given by
$P{V}^{\gamma }=$ Constant
Where,
$P=$ Pressure
$V=$Volume
$\gamma =\frac{C_p}{C_v}=1+\frac{2}{f}$
$C_p=$ Specific heat capacity at constant pressure.
$C_v=$ Specific heat capacity at constant volume.
$f=$ Degree of freedom

Slope of an adiabatic curve on $PV$ diagram $=-\gamma \frac{P}{V}$

A helium molecule is monoatomic in nature, which has three degrees of freedom and a carbon dioxide molecule is triatomic having six degree of freedom.
Therefore, for helium, we have $\gamma =\frac{5}{3}=1.67$ and for carbon dioxide, we have $\gamma =\frac{8}{6}=\mathrm{1.33.}$

The greater value of $\gamma$ represents a steeper $P-V$ curve. Therefore, curve $B$ represents helium.