First Law Efficiency:
The first law efficiency, also known as the energy efficiency or thermal efficiency, is a measure of how effectively a system converts input energy into useful output energy. It is defined as the ratio of the actual output energy to the input energy.

Exergy:
Exergy is a measure of the quality or usefulness of energy. It represents the maximum useful work that can be obtained from a system as it reaches equilibrium with its surroundings. Exergy takes into account both the quantity and the quality of energy.

Proper Utilization of Exergy:
To properly utilize exergy, it is desirable to maximize the exergy efficiency, which is the ratio of the useful exergy output to the input exergy. The exergy efficiency can be improved by minimizing the irreversibilities within a system.

First Law Efficiency and Source and Use Temperatures:
- First Law Efficiency: The first law efficiency is a measure of the energy conversion efficiency of a system. It represents the percentage of input energy that is converted into useful output energy. To maximize the first law efficiency, the system should be designed to minimize energy losses and maximize energy conversion.

- Source and Use Temperatures: The source and use temperatures refer to the temperatures at which energy is supplied to and extracted from a system. The temperature difference between the source and use temperatures determines the thermal efficiency of a system. The larger the temperature difference, the higher the thermal efficiency.

Desirable Conditions for Utilizing Exergy:
To properly utilize exergy, it is desirable to have the following conditions:
- First Law Efficiency as Close to Unity: A first law efficiency close to unity indicates that a large percentage of the input energy is converted into useful output energy. This implies that there are minimal energy losses within the system. Therefore, maximizing the first law efficiency is desirable for proper utilization of exergy.
- Source and Use Temperatures Match: When the source and use temperatures match, the temperature difference is minimized, resulting in higher thermal efficiency. This means that more of the input energy is converted into useful work. Therefore, matching the source and use temperatures is desirable for proper utilization of exergy.

Conclusion:
In conclusion, for proper utilization of exergy, it is desirable to have a first law efficiency as close to unity as possible and to match the source and use temperatures. These conditions minimize energy losses and maximize energy conversion, leading to a more efficient utilization of exergy.