Question

Which of the following statements is (are) true? a) When a system does work, its internal energy always decreases. b) Work done on a system always decreases its internal energy. c) When a system does work on its surroundings, the sign of the work is always positive. d) Positive work done on a system is always equal to the system's gain in internal energy. e) If you push on the piston of a gas-filled cylinder, the energy of the gas in the cylinder will increase.

Short answer

Based on the analysis of the given statements, identify which statements are true and which are false regarding work and internal energy. a) False - When a system does work, its internal energy does not always decrease. b) False - Work done on a system does not always decrease its internal energy. c) True - When a system does work on its surroundings, the sign of the work is always positive. d) False - Positive work done on a system is not always equal to the system's gain in internal energy. e) True - If you push on the piston of a gas-filled cylinder, the energy of the gas in the cylinder will increase.

Step-by-step solution

Statement a)

This statement claims that when a system does work, its internal energy always decreases. According to the first law of thermodynamics, the change in internal energy (∆U) is equal to the heat added to the system (Q) minus the work done by the system (W): ∆U = Q - W. When a system does work (W > 0), it is possible for its internal energy to decrease if the heat added (Q) is less than the work done. However, it is not true in every case since the heat added can be greater than the work done, leading to an increase in internal energy. Therefore, statement a is false.

Statement b)

This statement claims that work done on a system always decreases its internal energy. According to the first law of thermodynamics, if work is done on a system, it means that an external force is doing work on the system to increase its internal energy. In this case, the work done (W) is negative. The equation ∆U = Q - W would become: ∆U = Q + |W|. Since both Q and |W| are positive, the internal energy should increase. Therefore, statement b is false.

Statement c)

This statement claims that when a system does work on its surroundings, the sign of the work is always positive. According to the sign convention, when a system does work on its surroundings (expands), the work done is considered positive (W > 0). When surroundings do work on the system (compresses), the work done is considered negative (W < 0). Therefore, statement c is true.

Statement d)

This statement claims that positive work done on a system is always equal to the system's gain in internal energy. Positive work done on a system means it's done by the surroundings leading to an increase in the system's internal energy. But the first law of thermodynamics (∆U = Q - W) tells us that the change in internal energy depends on both the heat added (Q) and the work done (W) on the system. If positive work is done on the system, it can contribute to an increase in internal energy but it is not always equal to the total gain in internal energy because the heat added (Q) will also affect the internal energy. Therefore, statement d is false.

Statement e)

This statement claims that if you push on the piston of a gas-filled cylinder, the energy of the gas in the cylinder will increase. When you push the piston of a gas-filled cylinder, you are performing work on the system which is the gas inside the cylinder. As a result of this work, the internal energy of the gas in the cylinder will increase (provided that there is no heat loss during this process). Therefore, statement e is true. In conclusion: a) False b) False c) True d) False e) True

Key concepts

First Law of Thermodynamics

The First Law of Thermodynamics is a cornerstone principle of physics and chemistry. It is an expression of the conservation of energy. The law states that energy cannot be created or destroyed, only transformed from one form to another. This principle is vital when analyzing the behavior of systems in terms of heat and work exchanges, framed in the equation:\[ \Delta U = Q - W \]Where:

• \( \Delta U \) is the change in internal energy of the system.
• \( Q \) represents the heat added to the system.
• \( W \) denotes the work done by the system.

The equation emphasizes that any change in the system's internal energy is the result of energy transferred either as heat or work. This idea underpinned the analysis in the exercise, helping to determine the truth of each statement. Understanding this law helps students explore how various energy interactions, such as mechanical work on pistons or heat transfer in engines, affect a system's internal energy.

Internal Energy

Internal energy is an essential concept in thermodynamics, representing the total energy stored within a system. It includes kinetic energy, which depends on the motion of particles, and potential energy resulting from forces acting between particles. The internal energy changes when external factors, like work and heat, cause energy to flow in or out of the system:

• If heat is added to a system, the internal energy generally increases.
• If work is done by the system, its internal energy might decrease, depending on the heat input.
• Conversely, if work is done on the system, internal energy often increases.

In the exercise, evaluating each statement involved considering how changes in work and heat affect internal energy based on these principles. For example, pushing a piston into a gas-filled cylinder increases the gas's internal energy because work is being done on the system.

Work and Heat Transfer

Work and heat are two crucial ways energy can be transferred in thermodynamic processes.

• Work: In thermodynamics, work relates to energy transfer that results from a system's interaction with its surroundings. A system doing work on its surroundings will have a decrease in internal energy, unless balanced by incoming heat.
• Heat Transfer: Heat is a form of energy transfer that occurs due to temperature difference between the system and its surroundings.

The sign conventions in thermodynamics are significant:

• Work done by the system on its surroundings is considered positive.
• Work done on the system by its surroundings is considered negative.
The original exercise statements were assessed on how heat and work interact to alter a system's internal energy. For instance, when work is done on the system, more internal energy typically results if heat remains constant. Understanding these components is key for grasping the laws governing energy exchange in processes such as engine cycles or heating systems.