Question

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 = $\frac{1}{2} \times$isothermal curve slope

Answer 1

Answer: (C)

Adiabatic curve slope = $\gamma \times$ isothermal curve slope

Answer 2

For Isothermal process $PV =$constant

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

For adiabatic$PV^{\gamma} =$constant

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

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