**Adiabatic Process**

“A change in Pressure & Volume of gas in which temperature also changes is called an adiabatic process”.

### Essential Conditions for a perfect Adiabatic Process:

**1**. The walls of the container must be perfectly non conducting in order to prevent any exchange of heat between system & surroundings.

**2**. The process of compression & expansion should be sudden so that there is no time for the exchange of heat.

### Adiabatic Equation of a perfect gas:

If the volume of gas increases by an infinitesimal amount dV against an external pressure P, the external work was done by the gas in its expansion will be

dW = PdV ……………..(i)

dU = 1× C_{v} ×dT …………(ii)

where,

**C _{v} =** specific heat for one gm. mol of gas at constant volume.

Since , In adiabatic change, dQ =0

Therefore, we have

C_{v}dT +P.dV = 0 ……… (iii)

PV = RT, which on differentiation gives ,

P.dV + V.dP = RdT

C_{v}( P.dV +V.dP) /(R) + P.dV = 0

or, C_{v}(P.dV + V.dP) + R(P.dV) = 0

C_{p} – C_{v} = R

C_{v}(P.dV + V.dP) + (Cp – C_{v})P.dV = 0

or C_{v}.V.dP + C_{p}.P.dV = 0

dP/P +C_{p}dV/C_{v}V =0

But , C_{p}/C_{v} = γ

logP + γlogV = constant

log PV^{γ} = constant

or

**PV ^{γ} = constant ** ………(iv)

**The relation between T & V:**

RT/V.Vγ = constant

**TV**

^{γ-1}= constant

**Relation between T & P :**

P(RT/P)^{γ} = constant

**TP**

^{(1-γ)/γ}= constant

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