Isentropic Relations Calculator

Isentropic Temperature Ratio:

\[ t_2 = t_1 \times \left(\frac{p_2}{p_1}\right)^{\frac{\gamma-1}{\gamma}} \]

Initial Temperature (t1):

Final Pressure (p2):

Initial Pressure (p1):

Heat Capacity Ratio (γ):

dimensionless

Final Temperature (t2):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Isentropic Temperature Ratio?

The isentropic temperature ratio describes how temperature changes during an isentropic (constant entropy) process in thermodynamics. It's particularly important in analyzing compressible flows, gas turbines, and other thermodynamic systems.

2. How Does the Calculator Work?

The calculator uses the isentropic relation:

\[ t_2 = t_1 \times \left(\frac{p_2}{p_1}\right)^{\frac{\gamma-1}{\gamma}} \]

Where:

\( t_1 \) — Initial temperature (K)
\( t_2 \) — Final temperature (K)
\( p_1 \) — Initial pressure (Pa)
\( p_2 \) — Final pressure (Pa)
\( \gamma \) — Heat capacity ratio (cₚ/cᵥ), dimensionless

Explanation: This equation assumes an ideal gas undergoing a reversible, adiabatic process with constant specific heats.

3. Importance of Isentropic Relations

Details: Isentropic relations are fundamental in thermodynamics for analyzing compressors, turbines, nozzles, and diffusers. They help predict how temperature, pressure, and density relate during idealized processes.

4. Using the Calculator

Tips: Enter all values in consistent units (temperature in Kelvin, pressure in Pascals). The heat capacity ratio (γ) is typically 1.4 for air at standard conditions.

5. Frequently Asked Questions (FAQ)

Q1: What does isentropic mean?
A: Isentropic means constant entropy - a reversible, adiabatic process with no heat transfer.

Q2: What are typical values for γ?
A: For air, γ ≈ 1.4; for monatomic gases (He, Ar) γ ≈ 1.67; for diatomic gases (N₂, O₂) γ ≈ 1.4.

Q3: When is this relation valid?
A: For ideal gases with constant specific heats undergoing reversible, adiabatic processes.

Q4: How does temperature change with pressure?
A: For γ > 1, temperature increases with pressure in an isentropic compression and decreases with expansion.

Q5: What's the difference between isentropic and isothermal?
A: Isentropic processes involve temperature changes (no heat transfer), while isothermal processes maintain constant temperature (with heat transfer).