Question

The slopes of isothermal and adiabatic curves are related as

(a) Isothermal curve slope = adiabatic curve slope
(b) Isothermal curve slope = $\gamma X$ adiabatic curve slope
(c) Adiabatic curve slope = $\gamma X$ isothermal curve slope
(d) Adiabatic curve slope = $\frac{1}{2}X$ isothermal curve slope

• A. a
• B. b
• C. c
• D. d

Answer 1

The correct option is C c

For Isothermal process PV= constant
$\Rightarrow \left(\frac{dP}{dV}\right)=\frac{-P}{V}=$ Slope of Isothermal curve

For adiabatic $P{V}^{\gamma }$ = constant

$\Rightarrow \frac{dP}{dV}=\frac{-\gamma P}{V}=$ slop of adiabatic curve slope

Clearly, ${\left(\frac{dP}{dV}\right)}_{adiabatic}=\gamma {\left(\frac{dP}{dV}\right)}_{Isothermal}$