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, $P{V}^{\gamma }=$ constant
Again differentiating both side
$dP{V}^{\gamma }+\gamma V^{\gamma -1}dVP=0$ or $\frac{dP}{dV}=-\frac{P}{V}\times \gamma$
$\therefore$ slope of adiabatic curve $=\gamma \times$ slope of isothermal curve