Adiabatic Compression Temperature Calculator

Formula

The formula to calculate the final temperature during adiabatic compression is:

\[ T2 = T1 \cdot \left( \frac{P2}{P1} \right)^{\frac{\gamma - 1}{\gamma}} \]

Where:

\( T1 \) 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.
\( \gamma \) is the heat capacity ratio.

Example

Let's say the initial temperature (T1) is 300 K, the initial pressure (P1) is 100,000 Pa, the final pressure (P2) is 200,000 Pa, and the heat capacity ratio (γ) is 1.4. The final temperature would be calculated as follows:

\[ T2 = 300 \cdot \left( \frac{200000}{100000} \right)^{\frac{1.4 - 1}{1.4}} \approx 365.7 \text{ K} \]

So, the final temperature is approximately 365.7 K.

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.

Extended information about "Adiabatic-Compression-Temperature-Calculator"

Temperature Change in Adiabatic Compression

Definition: Adiabatic compression is a process in which a gas is compressed without exchanging heat with its surroundings, leading to a temperature change.

Formula: \( T_2 = T_1 \left( \frac{V_1}{V_2} \right)^{\gamma - 1} \)

\( T_2 \): Final temperature
\( T_1 \): Initial temperature
\( V_1 \): Initial volume
\( V_2 \): Final volume
\( \gamma \): Heat capacity ratio (Cp/Cv)

Example: \( T_2 = 300 \left( \frac{2}{1} \right)^{1.4 - 1} \)

Final temperature: \( T_2 \)
Initial temperature: \( T_1 = 300 \) K
Initial volume: \( V_1 = 2 \) m³
Final volume: \( V_2 = 1 \) m³
Heat capacity ratio: \( \gamma = 1.4 \)

Adiabatic Heat of Compression

Definition: The adiabatic heat of compression is the heat generated during the adiabatic compression of a gas.

Formula: \( Q = 0 \)

\( Q \): Heat (since no heat is exchanged in an adiabatic process)

Example: In an adiabatic process, \( Q = 0 \).

Heat: \( Q = 0 \)

Work Equation for Adiabatic Compression

Definition: The work done during adiabatic compression 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: \( W = \frac{100 \times 2 - 200 \times 1}{1.4 - 1} \)

Work done: \( W \)
Initial pressure: \( P_1 = 100 \) kPa
Initial volume: \( V_1 = 2 \) m³
Final pressure: \( P_2 = 200 \) kPa
Final volume: \( V_2 = 1 \) m³
Heat capacity ratio: \( \gamma = 1.4 \)

Adiabatic Temperature Rise Formula

Definition: The adiabatic temperature rise formula calculates the increase in temperature during adiabatic compression.

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

\( \Delta T \): Temperature rise
\( T_1 \): Initial temperature
\( P_1 \): Initial pressure
\( P_2 \): Final pressure
\( \gamma \): Heat capacity ratio (Cp/Cv)

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

Temperature rise: \( \Delta T \)
Initial temperature: \( T_1 = 300 \) K
Initial pressure: \( P_1 = 100 \) kPa
Final pressure: \( P_2 = 200 \) kPa
Heat capacity ratio: \( \gamma = 1.4 \)