Question

For an adiabatic process pVγ=k and after differentiating the equation we get that the slope of an adiabatic process is

dp/dV=−γp/V
For an isothermal process pV=k and after differentiating the equation we get that the slope of an isothermal process is
dp/dV=−p/V
It says in my book that during compression adiabatic curve is above the isothermal curve and that during expansion the vice versa happens. My question is that since the slope of the adiabatic process is γ times more than the slope of the isothermal process, shouldn't the curve of the former process always be above the latter?

Answer 1

The position of the adiabatic curve relative to the isothermal curve depends on whether the process is compression or expansion. During compression, the adiabatic curve is above the isothermal curve, whereas during expansion, the isothermal curve is above the adiabatic curve.

Step-by-step explanation:

In an adiabatic process, the slope of the curve is steeper than in an isothermal process. However, the position of the adiabatic curve relative to the isothermal curve depends on whether the process is compression or expansion. During compression, the adiabatic curve is above the isothermal curve, whereas during expansion, the isothermal curve is above the adiabatic curve.

This is because during compression, the pressure increases more rapidly in the adiabatic process compared to the isothermal process, resulting in the adiabatic curve being above. However, during expansion, the pressure decreases more rapidly in the adiabatic process, causing the isothermal curve to be above.