Question

Which of the following processes always results in an increase in the energy of a system? a) The system loses heat and does work on the surroundings. b) The system gains heat and does work on the surroundings. c) The system loses heat and has work done on it by the surroundings. d) The system gains heat and has work done on it by the surroundings. e) None of the above.

Short answer

a) The system loses heat and does work on the surroundings b) The system gains heat and does work on the surroundings c) The system loses heat and has work done on it by the surroundings d) The system gains heat and has work done on it by the surroundings e) None of the above Answer: d) The system gains heat and has work done on it by the surroundings.

Step-by-step solution

Option a: The system loses heat and does work on the surroundings.

In this case, both heat (q) and work (w) are taken away from the system, which means that q is negative and w is also negative. According to the first law of thermodynamics, ΔU = q + w. Since both q and w are negative, their sum will also be negative, meaning that the internal energy of the system decreases.

Option b: The system gains heat and does work on the surroundings.

Here, heat (q) gets added to the system, making it positive. However, the system is doing work (w) on the surroundings, taking energy away from it and making w negative. In this case, the change in internal energy is ΔU = q + w. Depending on the magnitudes of q and w, the internal energy may increase, decrease, or remain the same, so this option does not always result in increased energy.

Option c: The system loses heat and has work done on it by the surroundings.

In this situation, the system loses heat (q), resulting in a negative value for q. However, work (w) is being done on the system by the surroundings, which adds energy to the system and makes w positive. The change in internal energy is given by ΔU = q + w. Similar to option b, this option does not always result in increased energy since it depends on the magnitudes of q and w.

Option d: The system gains heat and has work done on it by the surroundings.

Here, the system gains heat (q) and has work done on it by the surroundings (w), which means that both q and w are positive. According to the first law of thermodynamics, ΔU = q + w. Because both q and w are positive, their sum will also be positive, leading to an increase in the system's internal energy. Therefore, this option will always result in an increase in the energy of a system.

Option e: None of the above.

We have found that option d always results in increased energy, so this option is not correct. In conclusion, the correct answer is option d) The system gains heat and has work done on it by the surroundings. This is the process that always results in an increase in the energy of a system.

Key concepts

Internal Energy

Internal energy is a key concept in the study of thermodynamics and refers to the total energy contained within a system. It is composed of several types of energies, including kinetic energy, due to the motion of the system's molecules, and potential energy, which is related to the intermolecular forces within the system.

Understanding how internal energy changes provides insight into the behavior of a system. When heat is added or work is done on a system, its internal energy increases. Conversely, if a system loses heat or does work on its surroundings, its internal energy decreases. This concept is fundamental in analyzing thermodynamic processes and is mathematically represented by the first law of thermodynamics as \( \Delta U = q + w \), where \( \Delta U \) is the change in internal energy, \( q \) is the heat added to or removed from the system, and \( w \) is the work done on or by the system.

Thermodynamic Processes

Thermodynamic processes involve the transfer of energy to or from a system and can include changes in temperature, volume, pressure, or internal energy. Such processes are often described in terms of heat transfer and work done.

There are several types of thermodynamic processes, including isothermal (constant temperature), isobaric (constant pressure), isochoric (constant volume), and adiabatic (no heat transfer). Each process type dictates how the internal energy, pressure, and volume of a system change, and it is important to understand these processes to predict the behavior of a system under various conditions. The ideal behavior of gases during these thermodynamic processes is often depicted by PV diagrams, which graph volume against pressure and demonstrate the work done on or by the system during a process.

Heat Transfer

Heat transfer is the movement of thermal energy from one object or system to another, driven by a temperature difference. It occurs through three main mechanisms: conduction, which involves direct molecular interaction; convection, which is the transfer of heat by the movement of fluids; and radiation, which is the transfer of energy by electromagnetic waves.

Understanding heat transfer is essential in thermodynamics, as it directly affects the internal energy of a system. The relationship between heat transfer and work in thermodynamic processes is encapsulated by the first law of thermodynamics. It is critical for students to grasp that heat transfer is not the same as temperature; instead, it is a measure of thermal energy flow, and it is considered positive when it enters a system and negative when it exits.

Work-Energy Principle

The work-energy principle is fundamental in both physics and thermodynamics. It states that work done on an object is equal to the change in its kinetic energy. In the context of thermodynamics, work can also relate to other forms of energy transfer, such as the expansion or compression of a gas in a system.

Work is a form of energy transfer that can either increase or decrease the internal energy of a system, depending on whether it is done on or by the system. Positive work is done on the system, leading to an increase in internal energy, while negative work is done by the system, leading to a decrease in internal energy. This principle is integral to solving problems that involve energy conversions and demonstrates the direct relationship between work and the internal energy state of a system.