Question

The increase in internal energy of the system is \(100 \mathrm{~J}\) when \(300 \mathrm{~J}\) of heat is supplied to it. What is the amount of work done by the system? (a) - 200 J (b) \(+200 \mathrm{~J}\) (c) \(-300 \mathrm{~J}\) (d) - 400 J

Short answer

The work done by the system is +200 J (option b).

Step-by-step solution

Understand the Problem

We need to determine the work done by the system when it absorbs heat and its internal energy changes. We know from the problem that the increase in internal energy is 100 J, and the heat supplied is 300 J.

Recall the First Law of Thermodynamics

The First Law of Thermodynamics is given by the equation \( \Delta U = Q - W \), where \( \Delta U \) is the change in internal energy, \( Q \) is the heat added to the system, and \( W \) is the work done by the system.

Insert Known Values into the Equation

We know \( \Delta U = 100 \text{ J} \) and \( Q = 300 \text{ J} \). Substituting these into the First Law equation gives:\[ 100 = 300 - W \]

Solve for Work Done

Rearrange the equation to solve for \( W \):\[ W = 300 - 100 \]This simplifies to \( W = 200 \text{ J} \).

Interpret the Result

Since the value of \( W \) is positive, this indicates that the work is done by the system. Therefore, the correct answer is \( +200 \text{ J} \), which corresponds to option (b).

Key concepts

First Law of Thermodynamics

The First Law of Thermodynamics is a fundamental concept in physics and serves as the cornerstone of energy conservation in thermodynamic processes. It's often expressed in the formula: \( \Delta U = Q - W \). In this equation:

• \( \Delta U \) represents the change in internal energy of a system.
• \( Q \) is the heat energy added to the system, which can warm it or cause it to do work.
• \( W \) is the work done by the system itself.

The First Law essentially states that the energy entering a system as heat, minus the energy leaving as work, is equal to the internal energy change of that system. This is a manifestation of the conservation of energy principle, ensuring energy can neither be created nor destroyed, only transformed. This leads to understanding how energy flows and transforms within a system and reinforces the idea that any increase in a system's internal energy must come from an added heat or a decrease in work done by the system.

Internal Energy

Internal energy is a key concept when discussing thermodynamics and energy transformations. It refers to the total energy contained within a system due to molecular motion, which includes both kinetic and potential energy components.

• Kinetic energy arises from the motion of molecules.
• Potential energy comes from the interactions between molecules.

Changes in internal energy are central to understanding many physical processes. In the context of the First Law of Thermodynamics, the internal energy changes as a result of heat added or removed from the system and the work executed by or on the system.
In our exercise, the system's internal energy increased by \(100 \text{ J}\). This change occurred because a portion of the supplied heat was used in doing work, while the rest contributed to increasing the system's internal energy.

Heat and Work

Heat and work are the two primary ways energy is transferred in and out of a thermodynamic system.
Heat (\( Q \)) can be thought of as the energy transfer resulting from a temperature difference between the system and its surroundings. It's often associated with heating up the system, causing temperature changes and phase transitions.
Work (\( W \)), on the other hand, generally involves energy being used to move the system's boundaries or produce motion. In thermodynamics, work done by the system might mean expanding against an external pressure, which requires energy.

• If work is done on the system, \( W \) is added to the internal energy.
• If the system does work on its surroundings, \( W \) is subtracted from \( Q \).

In our exercise, the system absorbed \(300 \text{ J}\) of heat, and after its internal energy increased by \(100 \text{ J}\), we determine that \(200 \text{ J}\) of energy was used to perform work, emphasizing the interplay between these elements.