First slide

Thermodynamic processes

Question

The slopes of isothermal and adiabatic curves are related as

Moderate

A

Isothermal curve slope = adiabatic curve slope
B

Isothermal curve slope = $γ \times$ adiabatic curve slope
C

Adiabatic curve slope = $γ \times$ isothermal curve slope
D

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

Solution

For Isothermal process $P V =$ constant
$\Rightarrow (\frac{d P}{d V}) = \frac{- P}{V} =$ Slope of Isothermal curve
For adiabatic $P V^{γ} =$ constant
$\Rightarrow \frac{d P}{d V} = \frac{- γ P}{V} =$ Slop of adiabatic curve slope
Clearly, ${(\frac{d P}{d V})}_{adiabatic} = γ {(\frac{d P}{d V})}_{Isothermal}$

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