Question

The relation between the slope of isothermal curve and slope of adiabatic curve

• A. slope of adiabatic curve $= \gamma$ times slope of isothermal curve
• B. slope of isothermal curve $= \gamma$ times slope of adiabatic curve
• C. slope of adiabatic curve $= \gamma^2$ times slope of isothermal curve
• D. slope of isothermal curve $= \gamma^2$ times slope of adiabatic curve

Answer 1

Answer: (A)

For isothermal process, $PV = $ constant
Differentiating both side
$PdV + VdP = 0$ or $\frac{dP}{dV} = \frac{-P}{V}$
Again for adiabatic process, $PV^\gamma =$ constant
Again differentiating both side
$dPV^\gamma + \gamma V^{\gamma-1} dV \, P = 0$ or $\frac{dP}{dV} = - \frac{P}{V} \times \gamma$
$\therefore $ slope of adiabatic curve $= \gamma \times$ slope of isothermal curve