Thermo engineering formula sheet
| Formula | Equation | Symbols | Conditions |
|---|---|---|---|
| Laws | |||
| First Law of Thermodynamics | Δ U = Q - W | ΔU Change in Internal Energy (J); Q Heat Added (J); W Work Done (J) | Sign convention: W is work done by the system |
| Ideal Gas Law 1 | PV = nRT | P Pressure (Pa); V Volume (m³); n Moles (mol); R Gas Constant (J/(mol·K)); T Temperature (K) | not defined |
| Combined Gas Law | P₁ V₁ / T₁ = P₂ V₂ / T₂ | P₁ Initial Pressure (Pa); V₁ Initial Volume (m³); T₁ Initial Temperature (K); P₂ Final Pressure (Pa); V₂ Final Volume (m³); T₂ Final Temperature (K) | Fixed amount of gas |
| Specific Heat Ratio | γ = c_p / (c_v) | γ Specific Heat Ratio; cₚ Specific Heat at Constant Pressure (J/(kg·K)); cᵥ Specific Heat at Constant Volume (J/(kg·K)) | γ ≈ 1.4 for air at standard conditions |
| Heat Transfer | |||
| Heat Transfer (Sensible) | Q = mcΔ T | Q Heat (J); m Mass (kg); c Specific Heat (J/(kg·K)); ΔT Temperature Change (K) | Constant specific heat; sensible heat only |
| Fourier Heat Conduction (1D) | Q = -k A dT / (dx) | Q Heat Transfer Rate (W); k Thermal Conductivity (W/(m·K)); A Cross-sectional Area (m²); dT/dx Temperature Gradient (K/m) | One-dimensional, steady conduction; sign indicates heat-flow direction |
| Newton's Law of Cooling | Q = hA(T_s - T_∞) | Q Heat Transfer Rate (W); h Convection Coefficient (W/(m²·K)); A Surface Area (m²); Tₛ Surface Temperature (K); T∞ Fluid Temperature (K) | Convection coefficient h assumed constant |
| Stefan-Boltzmann Radiation | Q = ε σ A T⁴ | Q Radiated Power (W); ε Emissivity; σ Stefan-Boltzmann Constant (W/(m²·K⁴)); A Surface Area (m²); T Temperature (K) | Net exchange requires a surrounding temperature term (T^4 - T_sur^4) |
Equations are rendered from the library's own typeset source with no term reordered, dropped or simplified. Symbol legends and validity conditions are the library's; an equation is a model, not a guarantee — confirm its assumptions hold before you rely on a result.
- The formula library records no validity conditions for this entry. An absent condition line is not a statement that the formula is unconditional — check the source before applying it outside the obvious case.
Reference values are provided for study and quick reference. Verify against current standards and manufacturer data before safety-critical design.