Question

The slopes of isothermal and adiabatic curves are related as

• A. Isothermal curve slope = adiabatic curve slope
• B. Isothermal curve slope = adiabatic curve slope
• C. Adiabatic curve slope = isothermal curve slope
• D.

Answer 1

The correct option is C

Adiabatic curve slope = isothermal curve slope

$\text{For Isothermal process PV}=constant\Rightarrow \frac{dP}{dV}=\frac{-P}{V}=\text{Slope of Isothermal curve}\text{For adiabatic}P{V}^{\gamma }=constant\Rightarrow \frac{dP}{dV}=\frac{-\gamma P}{V}=\text{Slope of adiabatic curve slope}Clearly,{\left(\frac{dP}{dV}\right)}_{adiabatic}=\gamma {\left(\frac{dP}{dV}\right)}_{Isothermal}$