Problem 26 - Chemistry in 30 days

Question

When a compressed gas is allowed to expand through a porous plug at a temperature above its inversion temperature, there is (a) a fall in temperature (b) a rise in temperature (c) neither a fall nor a rise in temperature (d) a fall in temperature first, followed by a rise

Step-by-Step Solution

Answer

(b) a rise in temperature.

Step 1: Understand the concept

This exercise is based on the Joule-Thomson effect, which describes the temperature change in a real gas when it is allowed to expand or compress without any heat exchange (adiabatically). The direction of the temperature change depends on its inversion temperature.

Step 2: Define inversion temperature

The inversion temperature is a specific temperature at which a gas neither cools nor warms during its expansion. For temperatures above the inversion temperature, the expansion through a porous plug or throttling results in a temperature change opposite to that at temperatures below the inversion temperature.

Step 3: Assess the effect above inversion temperature

According to the Joule-Thomson effect, for a gas kept at a temperature above its inversion temperature, when it expands adiabatically, it exhibits a rise in temperature. This is because the change undergoes a different behavior than when it is below the inversion temperature.

Step 4: Select the correct option

Given the described behavior of a gas expanding above the inversion temperature, the correct answer that aligns with our understanding is (b), a rise in temperature.

Key Concepts

Inversion Temperature

The inversion temperature is a vital element of the Joule-Thomson effect. It is the specific point at which a gas experiences no change in temperature during adiabatic expansion.
Below this temperature, a gas will cool as it expands, but above this threshold, the gas actually warms up. The concept hinges on the intermolecular forces present in gases:

• If the temperature is below the inversion temperature, these forces cause the gas to cool upon expansion.
• If the temperature is above, the forces result in a warming effect due to different molecular energy interactions.

Understanding inversion temperature is crucial for applications like refrigeration and air conditioning. Devices using gases need precise control of temperature states to function efficiently. Knowing the inversion temperature assists engineers in selecting gases with the desired cooling or warming properties for specific purposes.

Adiabatic Expansion

Adiabatic expansion refers to the process where a gas expands without exchanging heat with its surroundings. This means that no heat is transferred into or out of the system.
This concept is integral to understanding temperature changes in gases:

• As the gas expands adiabatically, it does work on its surroundings.
• The internal energy decreases because it uses up energy to perform this work.

The change in internal energy leads to a variation in temperature. Adiabatic processes are crucial in thermodynamics, especially in contexts involving natural gas distribution and the design of engines. Knowing how gases behave in such conditions allows for predicting and managing temperature changes without needing external heat exchange.

Temperature Change in Gases

Temperature change in gases during adiabatic processes like the Joule-Thomson effect relies on starting temperatures and the specific properties of the gas. This concept helps predict the results of expanding gases through processes like throttling—forcing gases through a small opening, such as a porous plug.
For a particular result of gas expansion:

• When below the inversion temperature, expansion typically cools the gas.
• When above the inversion temperature, expansion generally leads to heating.

By understanding these principles, one can predict the temperature behavior of gases in applications such as manufacturing and HVAC (Heating, Ventilation, and Air Conditioning). By managing temperature changes effectively, systems exploiting these effects can operate more efficiently and safely, catering to specific industrial and mechanical needs.