# Heat work and internal energy relationship

### Energy, Enthalpy, and the First Law of Thermodynamics Thermodynamics Part 1: Work, Heat, Internal Energy and Enthalpy Energy - The potential energy stored in the electrostatic bonding relationships among. The gas has internal energy, the temperature is the average KE. • if heat is added its internal energy increases. • if the gas expands and does work. To understand the relationship between work and heat, we need to understand a third, linking factor: the change in internal energy. Energy.

Eventually, the wire becomes hot enough to glow. Conversely, E is negative when the system does work on its surroundings. The sign conventions for heat, work, and internal energy are summarized in the figure below. The System and Work The system is usually defined as the chemical reaction and the boundary is the container in which the reaction is run.

In the course of the reaction, heat is either given off or absorbed by the system. Furthermore, the system either does work on it surroundings or has work done on it by its surroundings. Either of these interactions can affect the internal energy of the system. Chemical reactions can do work on their surroundings by driving an electric current through an external wire. Reactions also do work on their surroundings when the volume of the system expands during the course of the reaction The amount of work of expansion done by the reaction is equal to the product of the pressure against which the system expands times the change in the volume of the system.

Enthalpy Versus Internal Energy What would happen if we created a set of conditions under which no work is done by the system on its surroundings, or vice versa, during a chemical reaction? Under these conditions, the heat given off or absorbed by the reaction would be equal to the change in the internal energy of the system.

At constant volume, the heat given off or absorbed by the reaction is equal to the change in the internal energy that occurs during the reaction. Most reactions, however, are run in open flasks and beakers.

When this is done, the volume of the system is not constant because gas can either enter or leave the container during the reaction. The system is at constant pressure, however, because the total pressure inside the container is always equal to atmospheric pressure.

If a gas is driven out of the flask during the reaction, the system does work on its surroundings. If the reaction pulls a gas into the flask, the surroundings do work on the system.

We can still measure the amount of heat given off or absorbed during the reaction, but it is no longer equal to the change in the internal energy of the system, because some of the heat has been converted into work. We will therefore abbreviate the relationship between the enthalpy of the system and the internal energy of the system as follows. The piston moves inward, increasing internal pressure until the two pressures match. In this case we say that work is done on the gas. Unit analysis of the pressure-volume product shows that it has the same dimensions as energy: Volume behaves as a state function. Independent of any or all intermediate steps, the change in volume only depends on the initial and final readings.

Like other thermodynamic variables, internal energy exhibits two important properties: Being a state function means that E has the following property: Take as an example measuring volume changes. However the change in volume each time will be exactly the same no matter how many intermediate steps are taken. It is quite remarkable how much of chemistry is measured in a relative sense, that is, as a difference between two absolute values. The significance of state functions in difference measurements is profound.

Take for example measuring the energetics of a chemical reaction. If energy were not a state function, measurements would need to be made on each step of the process, including breaking the bonds of the reactants and reforming the bonds of the products.

### Internal Energy, Heat, and Work

Energy is also extensive or extrinsicmeaning it scales proportionally to the amount of material present. Other extensives include mass, volume, and pressure.

A property is intensive or intrinsic if it is independent of the amount of material. Intensives include the temperature and density of matter. Using a state function to analyze a gas being heated while being compressed. The relationship between the internal energy of a system and its heat and work exchange with the surroundings is: Interestingly, both q and w are not state functions.

They are path-dependent, meaning their values vary in magnitude according to how the work and heat are exchanged. They combine however, to form E, which is invariant to how the system is prepared. Consequently there is an interdependence between heat and work that we will now attempt to explore further. If a system is heated at constant volume, there is no chance for expansion work to occur and the internal energy expression simplifies to: Under conditions of constant pressure we will likewise define the constant pressure heat capacity CP. Laboratory chemistry takes place in an environment most suitable to study under the influence of the constant pressure supplied by the atmosphere, where we are required to include the work term in the internal energy expression.

When heating a gas against constant pressure there is a natural tendency for expansion. As a result, a portion of endothermic heat energy input into a system is not deposited as internal energy, but is returned to the surroundings as expansion work. Take for example a 1. Suppose the balloon is heated to a temperature of 50 o The change in internal energy of the gas is: Likewise during a constant-pressure exothermic process a system cools and contracts, so not all of the heat lost is stolen from internal energy, some is returned as the surroundings does work on the system to contract it. So why do we need a constant-volume heat capacity at all? To answer this, let us look at the special case of an ideal gas undergoing a change in its volume and heat content.

We will break the process up into two parts which we are allowed to do because of the properties of a state function.

• Internal energy

First we do an isothermal constant temperature change in volume. The ideal gas obeys kinetic theoryso its constituent particles have no potential energy of interaction of any kind. The kinetic energy they possess is a function of the temperature and mass of the particles.

## 1st Law of Thermodynamics

If the gas particles are allowed to expand or contract isothermally, they will be moved closer together or spread further apart while maintaining their same average velocities. Since they have no potential energy energy of positionthere is no change of internal energy due to their relocation. Introduction[ edit ] The internal energy of a given state of a system cannot be directly measured. It is determined through some convenient chain of thermodynamic operations and thermodynamic processes by which the given state can be prepared, starting with a reference state which is customarily assigned a reference value for its internal energy.

Sometimes, to that list are appended other extensive state variables, for example electric dipole moment. For practical considerations in thermodynamics and engineering it is rarely necessary or convenient to consider all energies belonging to the total intrinsic energy of a system, such as the energy given by the equivalence of mass. Customarily, thermodynamic descriptions include only items relevant to the processes under study. Thermodynamics is chiefly concerned only with changes in the internal energy, not with its absolute value.

The internal energy is a state function of a system, because its value depends only on the current state of the system and not on the path taken or processes undergone to prepare it. It is an extensive quantity. It is the one and only cardinal thermodynamic potential.