Question

Figure shows a curve on $\log T$ and $\log V$ scale, when an ideal gas is undergoing an adibatic process. The gas is

• A. Monatomic
• B. Diatomic
• C. Polyatomic
• D. Mixture of monatomic and diatomic

Answer 1

The correct option is A Monatomic

For an adiabatic process, equation of state in terms of $T$ and $V$ is given by
$T{V}^{\gamma -1}=k$
Taking logarithm on both sides,
$\log T+(\gamma -1)\log V=\log k$
$\Rightarrow \log T=-(\gamma -1)\log V+\log k$
Comparing this with $Y=mX+c$, we get,
Slope $m=-(\gamma -1)$
from the data given in the graph, we can say that
$-(\gamma -1)=\frac{2-4}{4-1}$
$\Rightarrow -(\gamma -1)=-\frac{2}{3}$
$\Rightarrow \gamma =\frac{5}{3}$
$\therefore$ Ideal gas is monoatomic in nature.
Thus, option (a) is the correct answer.