question_answer

The slopes of isothermal and adiabatic curves are related as

A) isothermal curve slope = adiabatic curve slope

B) isothermal curve slope =\[\gamma \]\[\times \]adiabatic curve slope

C) adiabatic curve slope =\[\gamma \]\[\times \]isothermal curve slope                 

D) adiabatic curve slope =\[\frac{1}{2}\]\[\times \]isothermal curve slope

Correct Answer: C

Solution :

[c] \[\frac{\text{Slope of adiabatic curve}}{\text{Slope of isothermal curve}}\] \[\text{=}\frac{{{\left( dP/dV \right)}_{adi}}}{{{\left( dP/dV \right)}_{iso}}}=+\gamma \] So slop to adiabatic curve is \[\gamma \left( =\frac{{{C}_{P}}}{{{C}_{V}}} \right)\] times of isothermal curve, as clear also from figure.