Question

The relation between the slope of isothermal curve and slope of adiabatic curve:

• A. Slope of adiabatic curve = $\gamma$ times slope of isothermal curve
• B. Slope of isothermal curve = $\gamma$ times slope of adiabatic curve
• C. Slope of adiabatic curve = ${\gamma }^2$ times slope of isothermal curve
• D. Slope of isothermal curve = ${\gamma }^2$ times slope of adiabatic curve

Answer 1

The correct option is A Slope of adiabatic curve = $\gamma$ times slope of isothermal curve

$PV=$ constant for isothermal process $=C$

$\therefore logP+logV=logC$

$\therefore$ Slope of $logP$ Vs $logV$ curves $=-1$

$P{V}^{\gamma }=$ constant for adiabatic process $K$

$\therefore logP+\gamma logV=logK$

$\therefore$ Slope of $logP$ Vs $logV$ curves $=-\gamma$

Hence, $\gamma \times$ Slope of isothermal curve $=$ Slope of adiabatic curves.