The value of \(\Delta E\) for a certain change is \(-1455 \mathrm{~J}\). During the change, the system absorbs \(812 \mathrm{~J}\) of heat. Did the system do work, or was work done on the system? How much work, expressed in joules, was involved?

Understanding how energy is stored in a system is foundational in the study of thermodynamics. This stored energy is referred to as internal energy, which can be conceptualized as the total of all the microscopic forms of energy of a system. Internal energy includes the kinetic energy due to the random motion of molecules, as well as potential energy arising from the forces between these particles.

Changes in internal energy can come about in two main ways: heat transfer and work done by or on the system. These are the avenues through which the energy of the system can increase or decrease. In the context of the exercise, a change in internal energy, denoted by \( \Delta E \) and given as \( -1455 \text{ J} \), indicates that the system's energy decreased by that amount during the process under consideration.

What is Heat?

Heat exchange refers to the transfer of thermal energy between a system and its surroundings due to a temperature difference. It's vital to recognize that heat is energy in transit, and it always flows from a region of high temperature to one of lower temperature until thermal equilibrium is reached.

In thermodynamics, heat is represented by the symbol \( q \) and is measured in joules (J). A positive value of \( q \) signifies that heat is absorbed by the system, contributing to an increase in the system's internal energy. Conversely, when \( q \) is negative, it implies that the system is losing heat to its surroundings.

In our exercise, the system absorbs \( 812 \text{ J} \) of heat, which partially counteracts the overall decrease in internal energy. This absorption of heat suggests external energy is being introduced into the system, impacting its state and potentially its physical properties.

The Role of Work in Energy Changes

Work done, denoted by \( w \) in thermodynamics, embodies the energy transfer that occurs when an external force is applied to a system causing its volume to change. Just like heat, work is also a transfer of energy and is measured in joules (J).

The sign convention for work can be initially confusing but is essential for solving problems correctly. When work is done on the system by the surroundings, \( w \) takes a positive value, indicating an input of energy to the system. If the system does work on the surroundings, \( w \) is negative - this scenario depicts the system expending energy.

In the case from our exercise, work done has a value of \( -2267 \text{ J} \). The negative sign tells us that the system exerted energy; it did work on its environment. This aligns with our physical understanding that if a system expands against an external pressure, for instance, it must use up internal energy to do so.