The ratio of the slopes of isothermal and adiabatic curves is

Step-by-step solution

For an isothermal change, (p V=K ) Differentiating both side, we get (p d V+V d p=0 V d p=-p d V ) ( ) Slope of an isothermal curve ( ( d p d V )_ iso =- p V ) For an adiabatic change, (p V^ =K^ ) Differentiating both side, we get ( aligned & p V^ -1 d V+V^ d p=0 & p d V+V d p=0 or V d p=- p d V aligned ) ( ) Slope of an adiabatic curve, ( aligned & ( d p d V )_ adia =- p V & ( d p d V )_ iso ( d p d V )_ adia = -p / V - p / V = 1 aligned )