Question

Why is the p.v. curve for an adiabatic process steeper than that for an isothermal process? Explain formation of clouds at night altitude.

Answer 1

Explanation:

For adiabatic process-

PVγ=constant

Differentiating above equation, we have

V γdP+P(γV γ−1dV)=0

⇒V γdP=−γPV γ−1 dV

⇒ dVdP=−γ VP

Hence the slope of adiabatic curve =−γ VP

For isothermal process-

PV=constant

Differentiating above equation, we have

VdP+PdV=0

⇒VdP=−PdV

⇒ dVdP=− VP

Hence the slope of isothermal curve =− VP

Therefore,

Slope of isothermal curve

Slope of adiabatic curve

= (− VP )(−γVP)=γ

As γ is always greater than 1, the slope of an adiabatic curve is greater than that of an isothermal curve by a factor of γ.

Hence the adiabatic curve is steeper than the isothermal curve, in both the processes of expansion and compression.