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 = \[\frac{1}{2}\times \]isothermal curve slope
Correct Answer: C
Solution :
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, \[{{\left( \frac{dP}{dV} \right)}_{\text{adiabatic}}}=\gamma {{\left( \frac{dP}{dV} \right)}_{\text{Isothermal }}}\]
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