# Show that Slope of Adiabatic Curve is more steeper than that of Isothermal Curve?

Slopes of Isothermal & Adiabatic Process
We know that for an Isothermal process :-

PV = K     ……..(i)
Differentiating eq.(i) we get ,

P△V + V△P = 0
or     P△V =  -V△P
or    △P/△V = -P/V …….(ii)

PV^γ= K    ……..(iii)

Differentiating eq.(iii) we get ,

γ.PV^γ-1△V + V^γ△P = 0
or     γ.PV^γ-1△V = – V^γ△P
or     △P/△V = – γ.PV^γ-1/ V^γ ……….(iv)
From eq. (ii) and (iv) , here γ > 1
It is clear that

{ Slope of adiabatic curve > Slope of Isothermal Curve }
∴ Adiabatic curve at any point is more steeper than Isothermal Curve.

The adiabatic & Isothermal curve in case of Compression & expansion are as follows :-
 Fig. (i) For expansion
 Fig (ii). For compression
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