1. Adiabatic vs. Polytropic

Compression adds energy to the gas.

• Adiabatic (Isentropic): Assumes perfect insulation (no heat loss) and reversible process. $PV^k = C$. Used as the reference for efficiency. Real compressors are never truly adiabatic because of friction and turbulence.
• Polytropic: The real-world process. Includes heat transfer and friction. $PV^n = C$. The exponent $n$ is determined experimentally. Typically $1 < n < k$ if cooled, or $n > k$ if irreversible losses dominate.

2. The Danger of Discharge Temp ($T_2$)

Compressing gas creates heat. The theoretical discharge temperature is: $$ T_2 = T_1 \left( \frac{P_2}{P_1} \right)^{\frac{n-1}{n}} $$ If $T_2$ exceeds 150-160°C, lubricating oil can break down or carbonize, and seals can fail. This sets the limit for the compression ratio per stage (usually max 3:1 or 4:1). If calculation shows $T_2 > 150^\circ C$, you need multi-stage compression with intercooling.

3. Mass Flow vs Volumetric Flow

Compressors are sized by inlet volume ($m^3/h$), but the work done depends on Mass ($\dot{m}$).
$\dot{m} = \rho_1 \times Q_1$.
Since $\rho_1 \propto P_1 / T_1$, a hot summer day (High $T_1$) reduces the mass flow capability of the machine, while a cold day increases it (and power demand!). This calculator derives mass flow internally.

4. Brake Horsepower (BHP)

The Gas Power (GHP) is the energy added to the gas.
The Brake Power (BHP) is what the motor must deliver to the shaft.
$BHP = GHP / \eta_{mech}$.
Mechanical losses (bearings, gears, seals) typically consume 2-5% of the power. This tool separates Gas Efficiency (Aerodynamic) from Mechanical Efficiency.