THERMODYNAMIC PROCESS OF PERFECT GAS

THERMODYNAMIC PROCESS OF PERFECT GAS: -

1. CONSTANT VOLUME PROCESS / ISOCHORIC PROCESS: - [n = ∞ ]

Follows Law – Gay-Lussac Law

P ∝ T (When V = Constant)

Heat Transferred Q_1-2 = (U₂ – U₁) = mC_v (T₂ –T₁)

Work Done dW = 0

Entropy Change dS = C_vln (T₂ / T₁)

 

2. CONSTANT PRESSURE PROCESS / ISOBARIC PROCESS: - [n = 0]

Follows Law – Charles’ Law

V ∝ T (When P = Constant)

Heat Transferred Q_1-2 = mC_p (T₂ –T₁)

Work Done dW = P (V₂ – V₁)

                              = mR (T₂ –T₁)

Internal energy dE = dQ – dW

                              =mC_p (T₂ –T₁) – mR (T₂ –T₁)

                              = mC_p (T₂ –T₁) – m (C_p – C_v) (T₂ –T₁)

                              = m C_v (T₂ – T₁)

Entropy Change dS = C_vln (T₂ / T₁)

3. CONSTANT TEMPERATURE PROCESS / ISOTHERMAL PROCESS: -[n = 1]

Follows Law – Boyel’s Law

P ∝ 1 / V (When T = Constant)

PV = CONSTANT.

Internal energy (dE) = 0

Fig.1 | Isothermal Process

dQ = dE + dW

= dW      [dE = 0]

= P. dV

1. P1V1 = PV P = P 1V1 / V

   = (P₁V₁ / V). dV

   
   
   
   = P₁V₁ ln(V₂/V₁)

    

   Heat Transferred dQ = dW = P₁V₁ ln(V₂/V₁) OR P₁V₁ ln(P₂ / P₁)

   Entropy Change dS = R ln(V₂/V₁)

4. ADIABATIC PROCESS OR ISENTROPIC PROCESS: - [n =γ ]

Follows Law –

PV^γ = CONSTANT.

Heat Transferred dQ = 0

Internal energy (dE) = - dW

dW = P. dV

    = (P₁V₁^γ / V^γ).dV

Fig.2 | Adiabatic process

Entropy Changes dS = 0

5. POLYTROPIC PROCESS: - [n =γ ]

Follows Law –

PVⁿ = CONSTANT.

Heat Transferred Q_1-2 = C_n (T₂ – T₁)

                                             = C_v (γ – n/ γ – 1) (T₂ - T₁)

                                             = (γ – n/ γ – 1) X Work Done

 

Work Done (W_1-2) = (P₁V₁ – P₂V₂) / n-1

Internal energy (dE) = mC_v (T₂ - T₁) 

Entropy Change dS =  

• FREE EXPANSION PROCESS: - When a fluid is allowed to expand suddenly in to a vacuum chamber through an orifice of  large dimension.

 Q_1-2 = 0 ;      W_1-2 = 0 ;    & dU = 0 

• THROTTLING PROCESS: - When a perfect gas is expanded through aperture of minute dimension (Slightly open valve)

Enthalpy remains constant.

 Q_1-2 = 0 ;      W_1-2 = 0 ;    & dU = 0 

READ - PROPERTIES OF GASES IN NON FLOW PROCESS