The slopes of isothermal and adiabatic curves | vedclass

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Question

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

Vedclass · Accepted Answer

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

Vedclass · Answer

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

The slopes of isothermal and adiabatic curves are related as

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