⚙️ Isentropic Processes & Polytropic
Analyze polytropic gas processes (PVn = C). Covers isobaric (n=0), isothermal (n=1), isentropic (n=γ), and isochoric (n→∞) as special cases. Compute W, Q, ΔU, ΔH, ΔS.
📝 Configuration
Key Equations:
PVn = constant
V₂ = V₁(P₁/P₂)1/n
T₂ = T₁(P₂/P₁)(n−1)/n
W = (P₂V₂ − P₁V₁)/(1−n) for n ≠ 1
W = P₁V₁ ln(V₂/V₁) for n = 1
Q = ΔU + W · ΔS = m[c_v ln(T₂/T₁) + R ln(V₂/V₁)]
PVn = constant
V₂ = V₁(P₁/P₂)1/n
T₂ = T₁(P₂/P₁)(n−1)/n
W = (P₂V₂ − P₁V₁)/(1−n) for n ≠ 1
W = P₁V₁ ln(V₂/V₁) for n = 1
Q = ΔU + W · ΔS = m[c_v ln(T₂/T₁) + R ln(V₂/V₁)]
📊 Results
Configure inputs and click Analyze to view results.
📘 Methodology
Polytropic Relation
A polytropic process follows PVn = C where n is the polytropic index. This general relation encompasses all quasi-static thermodynamic processes for an ideal gas in a single framework.
Special Cases
- n = 0: Isobaric (constant pressure)
- n = 1: Isothermal (constant temperature)
- n = γ: Isentropic (adiabatic reversible)
- n → ∞: Isochoric (constant volume)
Energy Analysis
First law for closed systems: Q = ΔU + W. For ideal gases, ΔU = mc_v ΔT and ΔH = mc_p ΔT. Entropy change uses the Gibbs relation for ideal gases: ds = c_v dT/T + R dv/v.