Question

(a) State the first law of thermodynamics. (b) What is meant by the internal energy of a system? (c) By what means can the internal energy of a closed system increase?

Short answer

(a) The first law of thermodynamics states that energy cannot be created nor destroyed, but only converted from one form to another within an isolated system, with the total energy remaining constant. It can be expressed as $$\mathrm{\Delta }U=Q-W$$. (b) The internal energy of a system refers to the total energy contained within the system, including the kinetic and potential energies of its individual particles. It is a state function. (c) The internal energy of a closed system can increase by heat transfer (positive Q) and work done on the system (positive W).

Step-by-step solution

(a) Define the first law of thermodynamics

The first law of thermodynamics, also known as the law of conservation of energy, states that energy cannot be created nor destroyed, but only converted from one form to another within an isolated system. In other words, the total energy of an isolated system remains constant. Mathematically, the first law of thermodynamics can be expressed as: $$\mathrm{\Delta }U=Q-W$$ where $\mathrm{\Delta }U$ represents the change in internal energy, $Q$ is the heat added to the system, and $W$ is the work done by the system.

(b) Define internal energy of a system

The internal energy of a system refers to the total energy contained within the system, which comprises of the kinetic and potential energies of its individual particles (atoms, molecules, or ions). This energy is associated with microscopic motion (vibrational, rotational, or translational) and interactions (chemical bonding or intermolecular forces) among the particles. The internal energy is a state function, which means it depends only on the current state of the system and not on the path or process taken to reach that state.

(c) Ways to increase internal energy of a closed system

There are primarily two ways by which the internal energy of a closed system can increase: 1. Heat transfer (denoted by Q): When heat is added to the system, the internal energy increases as the particles in the system absorb the energy, resulting in their increased motion or vibrational activity. 2. Work done on the system (denoted by W): When work is done on the system, energy is transferred to the system, resulting in an increase in its internal energy. For instance, compressing a gas requires work, and as a consequence, the internal energy of the gas increases. Keep in mind that a positive value for work indicates work done on the system, while a negative value represents work done by the system. So to increase the internal energy using work, the work value should be positive. It is important to note that for a closed system, the internal energy can decrease too if heat is removed from the system (negative Q) or if the system does work on the surroundings (positive W).

Key concepts

Internal Energy

At the microscopic level, every system holds energy within itself, known as internal energy. This encompasses both the kinetic energy, which is associated with the movement of particles such as atoms and molecules, and the potential energy that arises from forces that act between these particles. Think of internal energy as the total account balance of energy within a system; it increases with deposits (heat or work done on the system) and decreases with withdrawals (work done by the system or heat lost).
For a deeper grasp, imagine shaking a snow globe. The kinetic energy of the snowflakes whirling around is much like the individual particle movements inside a system, and their potential to settle back into place is akin to the potential energy within the system.
An important aspect of internal energy is that it's a state function. This means the current internal energy of a system doesn't care about its energy history; it's only tied to its present state, much like your current location doesn't reveal where you've been, just where you are now.

Conservation of Energy

An inviolable principle in physics is the conservation of energy, which asserts that energy can neither be created nor destroyed. It can only be transferred or transformed from one form to another. The law makes our universe's energy ledger balance, ensuring that the energy in a closed system is constant over time, similar to a checking account where the balance only changes when deposits or withdrawals (transfers) are made.
Imagine you're on a rollercoaster; as it climbs up, it's converting the mechanical energy from the motors (work) into potential energy. On descending, that potential energy changes back to kinetic energy. The amount of energy remains the same, simply changing forms. This concept is foundational in understanding the first law of thermodynamics, which applies the principle of conservation to the realm of thermal physics.

Heat Transfer

When discussing heat transfer, it's about the movement of energy due to a temperature difference. Heat can flow naturally from a warmer object to a cooler one, which is why a spoon in a hot cup of tea warms up over time. This transfer is a fundamental process by which a system's internal energy can be changed.
In terms of modes, heat can be transferred in three primary ways: conduction (direct contact), convection (fluid movement), and radiation (electromagnetic waves). The direction of heat transfer typically always moves towards restoring thermal equilibrium, that is balancing out temperature differences, just as water flows from higher to lower ground.
The concept of heat when related to thermodynamics is often depicted by the symbol Q. When heat enters a system, it adds to the internal energy (Q is positive), and when heat leaves a system, the internal energy decreases (Q is negative).

Work

In physics, work is defined as a force causing displacement. Essentially, whenever we exert a force that moves an object, we're doing work. In thermodynamics, work may not always be this obvious. For instance, compressing a gas within a piston does work on the gas, thereby increasing its internal energy. Similarly, allowing the gas to expand does work on the piston and surroundings, decreasing the gas's internal energy.
We use the symbol W to represent work in thermodynamic equations. Doing work on a system increases its internal energy (positive W), whereas work done by the system on its surroundings decreases it (negative W). This work interaction is a core component of the first law of thermodynamics, showcasing how energy can be converted from mechanical form to internal energy, and vice versa, keeping in mind the sacred rule of conservation.