Calculate the compression temperature, expansion temperature, or any of the initial values. Select the applicable tab for your use case.

Adiabatic Compression Temperature Calculator

Default tab is built for the most common use case: inlet temperature plus pressure change gives outlet temperature.

Compression Temp
Expansion Temp
Advanced Solver
Use absolute pressure values for gas-law calculations, such as psia, bara, kPaa, or absolute Pa.
Use Outlet Pressure
Use Compression Ratio
Use Outlet Pressure
Use Expansion Ratio
Enter any 4 values to solve the missing variable using the adiabatic relation.

Adiabatic Compression Temperature Formula

The following formula is used to calculate the final temperature during adiabatic compression. 

T2 = T1 * (P2 / P1) ^ {((γ - 1) / γ)}

Variables:

  • T1 is the initial temperature in Kelvin
  • T2 is the final temperature in Kelvin
  • P1 is the initial pressure in Pascals
  • P2 is the final pressure in Pascals
  • γ is the heat capacity ratio

To calculate the final temperature during adiabatic compression, multiply the initial temperature by the ratio of the final pressure to the initial pressure raised to the power of (γ - 1) / γ.

What is Adiabatic Compression?

Adiabatic compression is a process in which the pressure of a gas is increased without any heat exchange with the surroundings. During this process, the temperature of the gas increases as work is done on it. This type of compression is commonly observed in various thermodynamic cycles, such as those in internal combustion engines and refrigeration systems. The relationship between pressure and temperature during adiabatic compression is governed by the heat capacity ratio (γ), which is the ratio of the specific heat at constant pressure to the specific heat at constant volume.

How to Calculate Adiabatic Compression Temperature?

The following steps outline how to calculate the adiabatic compression temperature.

  1. First, determine the initial temperature (T1) in Kelvin.
  2. Next, determine the initial pressure (P1) in Pascals.
  3. Next, determine the final pressure (P2) in Pascals.
  4. Next, determine the heat capacity ratio (γ).
  5. Finally, calculate the final temperature (T2) using the formula T2 = T1 * (P2 / P1) ^ ((γ - 1) / γ).
  6. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Initial Temperature (T1) = 300 K

Initial Pressure (P1) = 100,000 Pa

Final Pressure (P2) = 200,000 Pa

Heat Capacity Ratio (γ) = 1.4