Question

Energy can be transferred from a system to its surroundings as work if (1) there is thermal equilibrium between system and surroundings (2) there is mechanical equilibrium between system and surroundings (3) if pressure of system $>$ atmospheric pressure (4) if pressure of system $<$ atmospheric pressure

Short answer

Options (3) and (4).

Step-by-step solution

Understand Energy Transfer

Energy can be transferred between a system and its surroundings in three main forms: heat, work, and mass. Focus on the condition specifying work transfer.

Review Thermal and Mechanical Equilibrium

Thermal equilibrium implies no temperature difference, thus no heat transfer occurs. Mechanical equilibrium entails no net force or pressure differences, preventing work transfer.

Analyze Pressure Conditions

Pressure differences drive work transfers. To transfer energy as work, the system’s pressure must not be equal to ambient pressure; it must either exceed or be less than it.

Identify Correct Pressure Condition

Energy can be transferred as work if there is a difference in pressure. Options (3) and (4) state such conditions, hence, correct.

Key concepts

thermal equilibrium

Thermal equilibrium occurs when two systems in thermal contact with each other stop exchanging heat because they have reached the same temperature. In simpler terms, it's like two glasses of water achieving the same warmth after being left in a room for a long time. When thermal equilibrium is reached, there is no further transfer of heat energy between the systems because the temperature difference is zero.
When we discuss energy transfer, especially in terms of work, thermal equilibrium means any heat energy exchange is non-existent. This is important in thermodynamics because it helps define conditions where only mechanical energy (work) can be transferred without the interference of thermal energy.
Hence, for work energy transfer focusing solely on mechanical interactions, the system and surroundings must either ignore or have already achieved thermal equilibrium.

mechanical equilibrium

Mechanical equilibrium means a state where no net forces are acting on a system, maintaining a constant state of motion without acceleration. Simply put, if the forces in a system balance out perfectly, we have mechanical equilibrium. For example, a book resting on a table where gravitational force is balanced by the table's support force.
In the context of energy transfer as work, mechanical equilibrium is significant because it creates a condition where there are no driving forces to perform work. To transfer energy as work, there must be an imbalance – pressure differences or unbalanced forces. If the system and surroundings are in mechanical balance, no work can be performed due to a lack of force differences.

pressure differences

Pressure differences are a major driving force for work transfer between a system and its surroundings. When there's a difference in pressure, it creates a potential for work – much like water flowing from a higher level to a lower level under the influence of gravity.
If the pressure inside a system is greater than the atmospheric pressure (outside), the system can expand, doing work on the surroundings. Conversely, if the system's pressure is less than the atmospheric pressure, the surroundings can do work on the system, compressing it.
This is crucial for understanding how energy can be transferred: without a pressure difference, no work can be done. Thus, for work transfer, the system's pressure must either exceed or be less than the external pressure – maintaining equality (mechanical equilibrium) would prevent any work energy transfer.

work transfer

Work transfer refers to the movement of energy between a system and its surroundings due to a force acting over a distance. In thermodynamics, this typically involves expansion or compression of gas within a system, leading to work being done by or on the system.
To facilitate work transfer, two essential conditions are:

• There must be a pressure difference between the system and surroundings. This pressure difference provides the necessary force.
• Either the system performs work on the surroundings (when its pressure is higher) or the surroundings perform work on the system (when its pressure is lower).

Therefore, understanding the pressure dynamics is crucial for predicting when and how work transfer can occur in a thermodynamic process.
In summary, pressure differences drive the capability to transfer energy as work, making it a pivotal concept in thermodynamic study.