Calculating the Final Temperature of a Gas in an Adiabatic Expansion

What is the final temperature of a gas in an adiabatic expansion?

A 1 mol of an ideal diatomic gas expands reversibly and adiabatically from 1 L to 32 L at 300 K. What is the final temperature of the gas in Kelvin?

Answer:

The final temperature of the gas in an adiabatic expansion can be calculated using the ideal gas law and the concept of adiabatic expansion. In this scenario, the final temperature of the gas is approximately 681.75 Kelvin.

In order to find the final temperature of the gas in an adiabatic expansion, we can utilize the ideal gas law equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.

Since the gas is expanding adiabatically, there is no heat transfer between the gas and its surroundings. This indicates that the process is reversible and the change in internal energy can be related to the work done by the gas.

By applying the equations for adiabatic expansion, we can determine the final temperature of the gas to be around 681.75 Kelvin. This calculation considers the initial and final volume, number of moles, and initial temperature of the gas.

Understanding the final temperature of a gas in an adiabatic expansion is crucial in analyzing thermodynamic processes and determining the behavior of gases under varying conditions.