Isothermal (T constant): ΔU = 0 ⇒ Q = W. W = nRT ln(V₂/V₁)

Adiabatic (Q = 0): ΔU = –W. PV^γ = constant, TV^γ–1 = constant. W = (P₁V₁ – P₂V₂)/(γ–1)

Isobaric (P constant): W = PΔV, Q = nC_pΔT

Isochoric (V constant): W = 0, Q = ΔU = nC_vΔT

Efficiency: η = 1 – T₂/T₁ = 1 – Q₂/Q₁ (maximum possible).

Work done: W = Q₁ – Q₂

Heat engine: η = W/Q₁ = 1 – Q₂/Q₁

Refrigerator: COP = Q₂/W = Q₂/(Q₁–Q₂)

Heat pump: COP = Q₁/W = Q₁/(Q₁–Q₂)

For Carnot refrigerator: COP_max = T₂/(T₁–T₂)

💡 NEET TIPS & SHORTCUTS

• For isothermal process, ΔU = 0, Q = W.
• For adiabatic process, Q = 0, ΔU = –W.
• In cyclic process, net work = area enclosed in PV diagram.
• C_p – C_v = R for ideal gases. γ = C_p/C_v = 1 + 2/f (f = degrees of freedom).
• For monatomic gas: f = 3, γ = 5/3; diatomic: f = 5, γ = 7/5; polyatomic: f = 6, γ = 4/3.

⚠️ COMMON MISTAKES

• Using C_v for isobaric process instead of C_p.
• Forgetting sign convention in First Law: ΔU = Q – W (work done BY system).
• Assuming adiabatic process means constant temperature – it's constant heat.
• Applying Carnot efficiency formula without converting temperatures to Kelvin.

First law: ΔU = Q – W

Isothermal work: W = nRT ln(V₂/V₁)

Adiabatic work: W = (P₁V₁ – P₂V₂)/(γ–1)

Efficiency (Carnot): η = 1 – T₂/T₁

C_p – C_v = R

γ = C_p/C_v