Calculate Temperature Change Adiabatic Expansion

Adiabatic Temperature Change Equation:

\[ \Delta T = T_1 \times \left[1 - \left(\frac{P_2}{P_1}\right)^{\frac{\gamma-1}{\gamma}}\right] \]

Initial Temperature (T1):

Initial Pressure (P1):

Final Pressure (P2):

Specific Heat Ratio (γ):

unitless

Temperature Change (ΔT):

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1. What is Adiabatic Temperature Change?

Adiabatic temperature change occurs when a gas expands or compresses without heat exchange with its surroundings. This process is fundamental in thermodynamics and describes how temperature changes with pressure in ideal gases under adiabatic conditions.

2. How Does the Calculator Work?

The calculator uses the adiabatic temperature change equation:

\[ \Delta T = T_1 \times \left[1 - \left(\frac{P_2}{P_1}\right)^{\frac{\gamma-1}{\gamma}}\right] \]

Where:

\( \Delta T \) — Temperature change (K)
\( T_1 \) — Initial temperature (K)
\( P_1 \) — Initial pressure (Pa)
\( P_2 \) — Final pressure (Pa)
\( \gamma \) — Specific heat ratio (cₚ/cᵥ)

Explanation: The equation describes how temperature changes during adiabatic expansion or compression of an ideal gas, where no heat is transferred to or from the system.

3. Importance of Adiabatic Calculations

Details: Adiabatic processes are crucial in understanding atmospheric phenomena, internal combustion engines, refrigeration cycles, and various engineering applications where rapid pressure changes occur without significant heat transfer.

4. Using the Calculator

Tips: Enter initial temperature in Kelvin, initial and final pressures in Pascals, and specific heat ratio (typically 1.4 for air, 1.67 for monatomic gases). All values must be positive with γ ≥ 1.

5. Frequently Asked Questions (FAQ)

Q1: What is the specific heat ratio (γ)?
A: γ is the ratio of specific heat at constant pressure (cₚ) to specific heat at constant volume (cᵥ). For air, it's approximately 1.4; for monatomic gases like helium, it's 1.67.

Q2: When is the adiabatic assumption valid?
A: The adiabatic assumption holds when the process occurs rapidly enough that heat transfer is negligible compared to the work done during compression or expansion.

Q3: What are typical applications of this equation?
A: Used in meteorology for atmospheric temperature changes, in engine design for compression cycles, and in various thermodynamic systems involving rapid gas expansion/compression.

Q4: How does temperature change during expansion vs compression?
A: During adiabatic expansion (P₂ < P₁), temperature decreases (ΔT negative). During adiabatic compression (P₂ > P₁), temperature increases (ΔT positive).

Q5: What are the limitations of this equation?
A: Assumes ideal gas behavior, adiabatic conditions (no heat transfer), and constant specific heat ratio. Real gases may deviate, especially at high pressures or temperatures.