Master Thermodynamics: P-V Diagrams & Carnot Efficiency

Apex Class • iitJEE Thermal Physics Lab

Thermodynamics P-V Indicator Diagrams & Carnot Engine Lab

Compare Isobaric, Isothermal, Adiabatic & Isochoric curves and master Carnot Efficiency (η)!

🔬 Expand from State A (P₀, V₀ = 150, 60) to Volume 2V₀. Select Process:

1. Isobaric (P = Const) 2. Isothermal (T = Const) 3. Adiabatic (Q = 0: Steeper!) 4. Isochoric (V = Const)

Governing Equation

V / T = Constant P V = Constant P V^γ = Constant P / T = Constant

Ideal Gas Law Form

Work Done (W = ∫ P dV)

P ΔV = n R ΔT (MAX) nRT ln(V₂ / V₁) (P₁V₁ – P₂V₂) / (γ – 1) 0 Joules (ΔV = 0)

W_isobaric > W_iso > W_adia > 0

P-V Curve Slope (dP/dV)

0 (Horizontal Flat) – (P / V) – γ (P / V) [Steeper!] ∞ (Vertical Line)

Slope_adia = γ × Slope_iso

Molar Heat Capacity (C)

C_p = (f/2 + 1) R C_iso = ∞ (Infinite) C_adia = 0 (Zero) C_v = (f/2) R

Polytropic PVⁿ: C = C_v + R/(1-n)

🔥 Carnot Efficiency η = 1 – (T_C / T_H) = W / Q_H. Select Carnot Scenario:

1. Carnot 4-Stroke P-V Loop 2. Standard Engine (600K → 300K: η=50%) 3. JEE Trap: Cool T_C vs Heat T_H by 100K 4. Carnot Refrigerator (COP = β)

Carnot Efficiency (η)

η = 1 – (T_C / T_H)

Also η = W / Q_H = 1 – Q_C/Q_H

Heat Ratio Law

Q_C / Q_H = T_C / T_H

Valid ONLY for Reversible Cycles

Refrigerator COP (β)

β = Q_C / W = T_C / ΔT

Where W = Q_H – Q_C

Degrees of Freedom (γ)

γ = 1 + (2 / f)

Mono: 5/3 | Dia: 7/5 | Poly: 4/3