Adiabatic Pressure Calculator

Formula

The formula to calculate the pressure or volume in an adiabatic process is:

\[ P_1 \cdot V_1^\gamma = P_2 \cdot V_2^\gamma \]

Where:

\( P_1 \) is the initial pressure.
\( V_1 \) is the initial volume.
\( P_2 \) is the final pressure.
\( V_2 \) is the final volume.
\( \gamma \) is the adiabatic index.

Example

Let's say the initial pressure (\( P_1 \)) is 100,000 Pa, the initial volume (\( V_1 \)) is 1 m³, the final volume (\( V_2 \)) is 0.5 m³, and the adiabatic index (\( \gamma \)) is 1.4. Using the formula:

\[ 100,000 \cdot 1^{1.4} = P_2 \cdot 0.5^{1.4} \]

We get:

\[ P_2 = \frac{100,000}{0.5^{1.4}} \approx 263901 \text{ Pa} \]

So, the final pressure (\( P_2 \)) is approximately 263901 Pa.

What is an Adiabatic Process?

An adiabatic process is a thermodynamic process in which there is no heat exchange between the system and its surroundings. This means that all the work done on or by the system results in a change in the internal energy of the system. In an adiabatic process, the temperature of the system can change even though no heat is added or removed. Adiabatic processes are commonly found in various natural and engineering systems, such as in the compression and expansion of gases in engines and refrigeration cycles.

Extended information about "Adiabatic-Pressure-Calculator"

Adiabatic Compression of Gas Calculator

Definition: Adiabatic compression is a process in which a gas is compressed without any heat exchange with its surroundings.

Formula: \( P_1 V_1^\gamma = P_2 V_2^\gamma \)

\( P_1 \): Initial pressure
\( V_1 \): Initial volume
\( P_2 \): Final pressure
\( V_2 \): Final volume
\( \gamma \): Heat capacity ratio (Cp/Cv)

Example: \( 100 \times 50^{1.4} = 200 \times 25^{1.4} \)

\( P_1 \): 100 kPa
\( V_1 \): 50 L
\( P_2 \): 200 kPa
\( V_2 \): 25 L
\( \gamma \): 1.4

Adiabatic Pressure Temperature Relation

Definition: The relation between pressure and temperature in an adiabatic process can be described by the Poisson's equation.

Formula: \( \frac{T_2}{T_1} = \left( \frac{P_2}{P_1} \right)^{\frac{\gamma - 1}{\gamma}} \)

\( T_1 \): Initial temperature
\( T_2 \): Final temperature
\( P_1 \): Initial pressure
\( P_2 \): Final pressure
\( \gamma \): Heat capacity ratio (Cp/Cv)

Example: \( \frac{T_2}{300} = \left( \frac{200}{100} \right)^{\frac{1.4 - 1}{1.4}} \)

\( T_1 \): 300 K
\( T_2 \): Final temperature
\( P_1 \): 100 kPa
\( P_2 \): 200 kPa
\( \gamma \): 1.4

How to Calculate Work for Adiabatic Process

Definition: The work done during an adiabatic process can be calculated using the initial and final states of the gas.

Formula: \( W = \frac{P_1 V_1 - P_2 V_2}{\gamma - 1} \)

\( W \): Work done
\( P_1 \): Initial pressure
\( V_1 \): Initial volume
\( P_2 \): Final pressure
\( V_2 \): Final volume
\( \gamma \): Heat capacity ratio (Cp/Cv)

Example: \( W = \frac{100 \times 50 - 200 \times 25}{1.4 - 1} \)

\( W \): Work done
\( P_1 \): 100 kPa
\( V_1 \): 50 L
\( P_2 \): 200 kPa
\( V_2 \): 25 L
\( \gamma \): 1.4

Equation for Adiabatic Process

Definition: The adiabatic process equation relates the pressure and volume of a gas undergoing an adiabatic change.

Formula: \( P V^\gamma = \text{constant} \)

\( P \): Pressure
\( V \): Volume
\( \gamma \): Heat capacity ratio (Cp/Cv)

Example: \( 100 \times 50^{1.4} = \text{constant} \)

\( P \): 100 kPa
\( V \): 50 L
\( \gamma \): 1.4

Formula for Adiabatic Process

Definition: The formula for an adiabatic process describes the relationship between pressure, volume, and temperature of a gas.

Formula: \( P V^\gamma = \text{constant} \)

\( P \): Pressure
\( V \): Volume
\( \gamma \): Heat capacity ratio (Cp/Cv)

Example: \( 150 \times 30^{1.4} = \text{constant} \)

\( P \): 150 kPa
\( V \): 30 L
\( \gamma \): 1.4