6.5
Quantifying Work
As a system undergoes a change, its internal energy can change, and energy can be transferred from the system to the surroundings, or from the surroun…
Recall that a system’s internal energy is defined as the sum of heat and work. Heat is measured using calorimetry, but how is work quantified?
Work is the result of a force, which an object experiences – such as by being pulled, pushed, or lifted – over a distance. Thus work equals force times distance.
If a golf club hits a ball 100 feet, then it has done work. Energy is transferred from the club to the ball.
In this case, the ball is the system on which work is performed by the surroundings.
In chemical reactions, work can be associated with multiple physical or chemical changes in a system. A commonly encountered type of work is pressure-volume work.
Consider the combustion in an engine’s cylinder. Not only does the combustion generate heat, it also produces gas, which performs work.
When the gas volume in the cylinder expands, the pressure pushes the piston downward acting against external forces in the surroundings.
Pressure is defined as a force acting over an area. Here, the force from the expanding gases is distributed over the area of the base of the piston. In other words, the force is pressure times area.
Thus, work, which is force times distance, can be rewritten as pressure multiplied by the area and distance over which it acts. For the engine cylinder, this is the height difference the piston moves.
Considering that area times height is the volume of a cylinder, the equation for work can be defined as pressure times the volume change of the system.
However, because the volume increases and the piston is pushed downward, the system actually performs work on the surroundings, which by convention is a negative value.
Therefore, work is defined as the negative of the pressure, P, times delta-V or the change in final and initial volume, which happened during the expansion.
The unit for pressure-volume work is usually defined as liter-atmosphere. This unit can be converted to the conventional unit of energy, Joules, by using the conversion factor one liter-atmosphere is equal to 101.3 Joules.
Q1: What is the basic definition of work in thermochemistry?
Work is defined as a force acting through a distance. In thermochemistry, when a system undergoes change, work represents energy transfer resulting from physical or chemical changes. For example, when a golf club strikes a ball 100 feet, the club performs work by transferring energy to the ball. Work is a key component alongside heat in determining changes to a system's internal energy.
Q2: How does pressure-volume work occur in a chemical system?
Pressure-volume work occurs when a system pushes against external pressure or when surroundings compress the system. In an engine cylinder, combustion produces expanding gases that push the piston downward. The expanding gas exerts pressure (force per unit area) against the piston, performing work on the surroundings. This type of work is the most commonly encountered in chemical reactions involving volume changes.
Q3: Why is the work equation for gas expansion written with a negative sign?
The negative sign in the work equation reflects the sign convention for energy transfer. When a system expands and performs work on the surroundings, the system loses energy, so work is assigned a negative value. Mathematically, since volume increases during expansion (ΔV is positive), the negative sign ensures work is negative, indicating energy leaves the system and goes to the surroundings.
Q4: What is the mathematical relationship between pressure, volume, and work?
Work equals pressure multiplied by the change in volume: w = -PΔV. This derives from the fundamental equation work equals force times distance. Since pressure is force per unit area and area times distance equals volume change, the product of pressure and volume change yields work. This relationship allows chemists to calculate work from measurable pressure and volume data in chemical systems.
Q5: How do you convert pressure-volume work units to Joules?
Pressure-volume work is typically expressed in liter-atmospheres (L·atm), which must be converted to Joules for standard energy calculations. The conversion factor is one liter-atmosphere equals 101.3 Joules. To convert, multiply the work value in L·atm by 101.3 to obtain the equivalent energy in Joules, the conventional unit for thermochemical calculations.
Q6: How does an internal combustion engine demonstrate pressure-volume work?
In an engine, combustion of gasoline and oxygen is exothermic, releasing energy as both heat and work. The expanding gases in the cylinder push the piston outward against external pressure. The substances undergoing reaction form the system, while the engine and surroundings form the external environment. The system loses internal energy through both heat release and work performed on the surroundings.
Q7: How does pressure relate to force and area in work calculations?
Pressure is defined as force distributed over an area. In work calculations, the force from expanding gases in a cylinder is expressed as pressure times the piston's base area. Since work equals force times distance, and area times distance equals volume change, pressure-volume work emerges as the practical equation for quantifying work in chemical systems undergoing expansion or compression.