Question

A substance whose Joule-Thomson coefficient is negative is throttled to a lower pressure. During this process, (select the correct statement) \((a)\) the temperature of the substance will increase. (b) the temperature of the substance will decrease. \((c)\) the entropy of the substance will remain constant. \((d)\) the entropy of the substance will decrease. \((e)\) the enthalpy of the substance will decrease.

Short answer

" Answer: (a) The temperature of the substance will increase.

Step-by-step solution

Understanding the Joule-Thomson Coefficient

The Joule-Thomson coefficient (denoted as µ) is defined as the change in temperature (T) with respect to change in pressure (P) at constant enthalpy (H). Mathematically, it is expressed as: µ = (∂T/∂P)_H.

Positive vs Negative Joule-Thomson Coefficient

For a gas with a positive Joule-Thomson coefficient, when it is throttled, its temperature decreases as the pressure decreases. Conversely, for a gas with a negative Joule-Thomson coefficient, its temperature increases as the pressure decreases during the throttling process. Since in this exercise the substance has a negative Joule-Thomson coefficient, we can immediately identify the correct statement \((a)\): the temperature of the substance will increase.

Entropy Change During Throttling Process

Throttling is an isenthalpic process, meaning that the enthalpy remains constant throughout this process. For an ideal gas, entropy change depends only on the change in temperature and volume. An increase or decrease in temperature will result in a change in entropy, so the entropy of the substance will not remain constant. We can eliminate option \((c)\).

Entropy Decrease or Not

We know that entropy change is not constant, but we cannot conclude if it increases or decreases without information on the specific substance and initial and final states. So, we cannot choose option \((d)\) as our answer.

Enthalpy Change During Throttling Process

As mentioned in step 3, the throttling process is an isenthalpic process, which means that the enthalpy (H) remains constant. Therefore, the enthalpy of the substance will not decrease, and we can eliminate option \((e)\).

Result:

Based on the analysis and steps above, the correct statement is: \((a)\) the temperature of the substance will increase.

Key concepts

Isenthalpic Process

An isenthalpic process is one where the enthalpy of the system remains constant. Enthalpy, represented with the symbol H, is a measure of the total energy of a thermodynamic system, including both internal energy and the energy associated with pressure and volume.

In the context of our exercise, throttling is an example of such a process. When a substance is throttled, it means that it is forced through a valve or porous plug, which causes a drop in pressure but does not allow heat exchange with the environment. This aspect of throttling leads to a constant enthalpy condition because no work is done by or on the system, and no heat is transferred, assuming ideal behavior.

Importance in Thermodynamics

Understanding an isenthalpic process is essential for dealing with real-life thermodynamic operations such as the flow of refrigerants in cooling systems or the expansion of gases through turbines. These practical applications often require analyzing conditions under which energy is conserved in such a specific form.

Entropy Change

Entropy, symbolized as S, is a key concept in thermodynamics, representing the degree of disorder or randomness in a system. A change in entropy usually indicates an energy transformation or a heat transfer, with higher entropy signifying greater disorder.

During a throttling process, although the enthalpy remains unchanged, there can be a change in entropy. For ideal gases, this change relates to the temperature and volume variation of the gas — as the gas expands and its temperature changes, the randomness of the molecular motion increases or decreases, thus changing the entropy.

Understanding Entropy in Processes

Entropy change helps in determining the direction of heat transfer and the feasibility of a process. In a real-world scenario, understanding entropy change enables the prediction of efficiency for systems like engines, refrigerators, and heat pumps, making this concept a cornerstone of engineering and physics.

Throttling Process

A throttling process, also known as a Joule-Thomson expansion, is an irreversible process where a fluid is expanded from higher to lower pressure through a restriction, like a valve or a porous plug, without any work being done by or on the fluid and without any heat being transferred to the surroundings.

This process is characterized by its isenthalpic nature — meaning the enthalpy of the fluid remains constant throughout the process. However, even with constant enthalpy, the temperature and entropy of the substance can change. If the Joule-Thomson coefficient of the substance is negative, as in our exercise, the temperature will increase upon expansion, as the internal energy of the fluid converts to kinetic energy.

Practical Relevance of Throttling

The throttling process is integral to various industrial applications, including air conditioners and refrigerators, where the expansion valve acts as the throttling device. By exploiting the temperature change associated with throttling, these systems can effectively transfer heat to achieve cooling.