Methods of Heating and Expanding Gases
Methods of Heating and Expanding Gases (Not Vapours) Table
| Type of expansion |
Remarks |
Work done (W) |
Change of internal energy (E) |
Heat absorbed (H) |
Final temperature |
| Constant pressure |
Isobar |
P(V₂ - V₁) |
M Cᵥ (T₂ - T₁) |
M Cₚ (T₂ - T₁) |
T₁ (V₂ / V₁) |
| Constant temperature |
Isotherm |
P₁ V₁ logₑ (V₂ / V₁) |
0 |
P₁ V₁ logₑ (V₂ / V₁) |
T₁ |
| Constant heat |
Adiabatic, PVⁿ = const. |
(P₁ V₁ - P₂ V₂) / (γ - 1) |
M Cᵥ (T₂ - T₁) |
0 |
T₁ (V₁ / V₂)γ-1 |
| Int. energy & temperature change |
Polytrope, PVⁿ = const. |
(P₁ V₁ - P₂ V₂) / (n - 1) |
M Cᵥ (T₂ - T₁) |
W + E |
T₁ (V₁ / V₂)n-1 |
where
W = external work done by gas (kJ)
E = increase of internal energy by gas (kJ)
H = total heat absorbed (kJ)
P₁, P₂ = initial, final, pressure (N/m²)
V₁, V₂ = initial, final, volume (m³)
T₁, T₂ = initial, final, temperature (°C)
M = mass (kg)
γ = Cₚ / Cᵥ (dimensionless)
n = index of expansion law (dimensionless)
Cᵥ = specific heat capacity at constant volume (kJ/kg K)
Cₚ = specific heat capacity of constant pressure (kJ/kg K)
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