Q. The slopes of isothermal and adiabatic curves are related as
A) Isothermal curve slope = adiabatic curve slope
B) Isothermal curve slope $= \gamma \times$ adiabatic curve slope
C) Adiabatic curve slope $= \gamma \times$ isothermal curve slope
D) Adiabatic curve slope $= 1/2 \times$ isothermal curve slope
Explanation
(c) For Isothermal process $PV =$ constant
$\Rightarrow \left( \frac{dP}{dV} \right) = \frac{- P}{V} =$ Slope of Isothermal curve
For adiabatic $PV^{\gamma} =$ constant
$\Rightarrow \frac{dP}{dV} = \frac{- \gamma P}{V} =$ Slope of adiabatic curve
Clearly, $\left( \frac{dP}{dV} \right)_{adibatic} = \gamma\left( \frac{dP}{dV} \right)_{Isothermal}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.