Problem 24 - Chemistry The Central Science In Si Units

Question

(a) Write an equation that expresses the first law of thermodynamics in terms of heat and work. (b) Under what condi. tions will the quantities \(q\) and \(w\) be negative numbers?

Step-by-Step Solution

Answer

(a) \( \Delta U = q + w \); (b) \( q \) is negative when heat is released, and \( w \) is negative when work is done by the system.

Step 1: Understanding the First Law of Thermodynamics

The first law of thermodynamics is a statement of the conservation of energy. It states that energy can neither be created nor destroyed, only transformed from one form to another. In terms of internal energy, heat, and work, this law can be expressed using an equation.

Step 2: Expressing the First Law in an Equation

The equation that represents the first law of thermodynamics in terms of internal energy change, heat, and work is given by: \( \Delta U = q + w \), where \( \Delta U \) is the change in internal energy of the system, \( q \) is the heat added to the system, and \( w \) is the work done on the system.

Step 3: Understanding When \( q \) is Negative

The quantity \( q \) is negative when heat is released from the system to the surroundings. This often occurs in exothermic processes, where the system loses heat as it transforms energy into work or other forms.

Step 4: Understanding When \( w \) is Negative

The quantity \( w \) is negative when work is done by the system on its surroundings. This typically occurs when the system expands, such as in the case of an expanding gas pushing against a piston.

Key Concepts

First Law of Thermodynamics

The first law of thermodynamics is a fundamental principle, pivotal in understanding energy interactions in physical systems. It asserts that energy cannot be created or destroyed; it can only change forms. In simpler terms, this law emphasizes the continuous balance of energy. When energy enters or leaves a system, it does so either as heat or as work. This conservation principle can be represented using an equation: \[ \Delta U = q + w \]Here, \( \Delta U \) represents the change in internal energy of the system, \( q \) denotes heat added to the system, and \( w \) is work done on the system. This equation ties together internal energy, heat, and external work, providing a complete account of energy transformations.

Conservation of Energy

Conservation of energy is the underlying theme of the first law of thermodynamics. It dictates that the total energy of an isolated system remains constant. In practical scenarios:

• Energy can be transferred between a system and its surroundings.
• It can change forms, but the total energy count never changes.

The conservation of energy ensures that any energy "lost" by a system is "gained" by its surroundings, and vice versa. This balancing act is crucial in processes like chemical reactions, engine operations, and even biological metabolism.

Internal Energy

Internal energy encompasses all the energy contained within a system. It includes kinetic energies of particles, potential energy in chemical bonds, and more. As a dynamic component:

• Internal energy changes when heat is transferred in or out of a system (heat, \( q \)).
• It also changes when work is performed by or on the system (work, \( w \)).

The internal energy change is central to understanding how energy transactions occur within a system, reflected in the equation \( \Delta U = q + w \). By observing changes in internal energy, one can infer whether a system is gaining or losing energy.

Heat and Work

Heat and work are the two primary mechanisms through which energy is exchanged between a system and its surroundings. They play distinctive roles:- **Heat (\( q \))**: - Represents energy transfer due to temperature difference. - Is positive when heat enters the system. - Is negative when the system releases heat (e.g., during cooling processes).- **Work (\( w \))**: - Occurs when forces act over distances, changing the system's energy. - Is positive when work is done on the system. - Is negative when the system performs work on its surroundings (e.g., gas expansion pushing a piston).Together, heat and work explain the flow and transformation of energy within thermodynamic systems. Recognizing whether these values are negative or positive helps determine the direction and impact of energy changes.