**Slopes of Isothermal & Adiabatic Process**

We know that for an Isothermal process :-

PV = K ……..(i)

PV = K ……..(i)

Differentiating eq.(i) we get ,

P△V + V△P = 0

P△V + V△P = 0

or P△V = -V△P

or △P/△V = -P/V …….(ii)

Differentiating eq.(iii) we get ,

γ.PV^γ-1△V + V^γ△P = 0

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 }

{ 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 |

For any query, feedback, suggestions write to us in comment section.

Thanks.good write.