Question

The gas in a piston (defined as the system) warms and absorbs \(655 \mathrm{~J}\) of heat. The expansion performs \(344 \mathrm{~J}\) of work on the surroundings. What is the change in internal energy for the system?

Short answer

The change in internal energy for the system is \(311 \mathrm{~J}\).

Step-by-step solution

Identify the Known Values

Recognize the values given in the problem: amount of heat absorbed by the system, represented as Q, is 655 J, and the work done by the system on the surroundings, represented as W, is 344 J.

Understand the First Law of Thermodynamics

The first law of thermodynamics is given by the equation \(\Delta U = Q - W\), where \(\Delta U\) stands for the change in internal energy of the system, Q represents the heat added to the system, and W is the work done by the system.

Apply the First Law of Thermodynamics

Substitute the known values into the equation to find the change in internal energy: \(\Delta U = 655 \mathrm{~J} - 344 \mathrm{~J}\).

Calculate the Change in Internal Energy

Perform the subtraction to calculate the change in internal energy: \(\Delta U = 655 \mathrm{~J} - 344 \mathrm{~J} = 311 \mathrm{~J}\).

Key concepts

Thermodynamics

Thermodynamics is a branch of physics that deals with heat, work, temperature, and the interrelationships among them. It typically involves studying systems and understanding how energy transformations can occur within them. This area of science lays out fundamental principles, such as the laws of thermodynamics, that govern the flow and conversion of energy.

In the context of textbook exercises, thermodynamics can explain various physical phenomena, such as the behavior of gases under different conditions of temperature and pressure. For example, when we talk about a gas in a piston that warms and absorbs energy, we're discussing a thermodynamic process in which energy is transferred to the gas, resulting in changes to its thermal condition and mechanical work being performed by the system.

Internal Energy

Internal energy is a term used in thermodynamics to describe the total energy contained within a system due to the microscopic motions and interactions of its particles. This energy includes kinetic energy from the motion of particles and potential energy from the forces that act within the system, such as molecular or atomic forces.

The internal energy is a state function, meaning it depends only on the current state of the system and not on the path the system took to reach that state. In physics problems like our textbook example, we calculate the change in internal energy (\(\Delta U\)) when a gas absorbs heat or performs work. This change is key to understanding how the energy of the system has been altered as a result of the thermodynamic process.

Heat Transfer

Heat transfer is the movement of thermal energy from one object or system to another, driven by a difference in temperature. It can occur through various means, including conduction, convection, and radiation.

In thermodynamic exercises, heat transfer is often represented by the variable Q. When a system, such as our gas in a piston, absorbs heat, we say that Q is positive, indicating that the system has gained energy. This gained energy can change the system’s properties, such as temperature or volume, and play a central role in the calculations of thermodynamic processes.

Work Done

Work done in thermodynamics refers to the energy transferred when a force acts on an object through a distance. It’s a central concept that connects mechanical action to energy changes within a system. The key equation for work done by a system is W = F * d, where F represents force, and d represents displacement.

In our piston example, the system does work on its surroundings when it expands, signified by the variable W. When a gas does work by expanding, it typically results in a mechanical effect, like moving a piston, and this work done by the system is usually associated with energy leaving the system. Therefore, calculating the work done helps us to quantify part of the energy change during a thermodynamic process.