Question

Which of the following is true regarding reversible adiabatic expansion of an ideal gas?

• A. Plot of $T$ vs $V$ is a straight line with slope equal to $\gamma$
• B. Plot of ln $T$ vs ln $V$ is a straight line with slope equal to $\gamma$.
• C. Plot of ln $T$ vs ln $V$ is a straight line with slope equal to $-\gamma$
• D. Plot of ln $T$ vs ln $V$ is a straight line with slope $(1-\gamma )$

Answer 1

The correct option is D Plot of ln $T$ vs ln $V$ is a straight line with slope $(1-\gamma )$

For an adiabatic process

$T{V}^{\gamma -1}=cons$

$T\propto V^{1-\gamma }$

Graphical approach

$T=[1-\gamma ]V$

$y=\left[m\right]x$ , so slope is $1-\gamma$