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Kurs: Chemia - program rozszerzony > Rozdział 10
Lekcja 1: Energia wewnętrznaPressure-volume work
The meaning of work in thermodynamics, and how to calculate work done by the compression or expansion of a gas
Key Points:
- Work is the energy required to move something against a force.
- The energy of a system can change due to work and other forms of energy transfer such as heat.
- Gases do expansion or compression work following the equation:
Introduction: Work and thermodynamics
When people talk about work in day-to-day conversation, they generally mean putting effort into something. You might "work on a school project" or "work to perfect your baseball pitch." In thermodynamics, however, work has a very specific meaning: it is the energy it takes to move an object against a force. Work, , is one of the fundamental ways energy enters or leaves a system, and it has units of Joules ( ).
When a system does work on the surroundings, the system's internal energy decreases. When a system has work done on it, the internal energy of the system increases. Like heat, the energy change from work always occurs as part of a process: a system can do work, but doesn't contain work.
To calculate work done by a constant force, we can use the following general equation:
.
For the purposes of chemistry class (as opposed to physics class), the most important takeaway from this equation is that work is proportional to the displacement as well as the magnitude of the force used. Different versions of the work equation can be used depending on the type of force involved. Some examples of doing work include:
- A person lifting books from the ground to a shelf does work against gravity.
- A battery pushing electrical current through a circuit does work against resistance.
- A child pushing a box along the floor does work against friction.
In thermodynamics, we are mainly interested in work done by expanding or compressing gases.
Pressure-volume work: Work done by a gas
Gases can do work through expansion or compression against a constant external pressure. Work done by gases is also sometimes called pressure-volume or PV work for reasons that will hopefully become more clear in this section!
Let's consider gas contained in a piston.
If the gas is heated, energy is added to the gas molecules. We can observe the increase in average kinetic energy of the molecules by measuring how the temperature of the gas increases. As the gas molecules move faster, they also collide with the piston more often. These increasingly frequent collisions transfer energy to the piston and move it against an external pressure, increasing the overall volume of the gas. In this example, the gas has done work on the surroundings, which includes the piston and the rest of the universe.To calculate how much work a gas has done (or has done to it) against a constant external pressure, we use a variation on the previous equation:
where is the external pressure (as opposed to the pressure of the gas in the system) and is the change in the volume of the gas, which can be calculated from the initial and final volume of the gas:
Since work is energy, it has units of Joules (where ). You may also see other units used, such as atmospheres for pressure and liters for volume, resulting in as the unit for work. We can convert to convert to Joules using the conversion factor of .
The sign of work
As a matter of convention, negative work occurs when a system does work on the surroundings.
- When the gas does work the volume of a gas increases (
) and the work done is negative. - When work is done on the gas, the volume of the gas decreases (
) and work is positive.
One way to remember the sign convention is to always think about the change in energy from the point of view of the gas. When the gas expands against an external pressure, the gas has to transfer some energy to the surroundings. Thus, the negative work decreases the overall energy of the gas. When the gas is compressed, energy is transferred to the gas so the energy of the gas increases due to positive work.
Example: Calculating work done on a gas
To illustrate how to use the equation for PV work, let's imagine a bicycle pump. We will assume that the air in the bicycle pump can be approximated as an ideal gas in a piston. We can do work on the air in the pump by compressing it. Initially, the gas has a volume of . We apply a constant external pressure of to push down the handle of the bike pump until the gas is compressed to a volume of . How much work did we do on the gas?
We can use the equation from the previous section to calculate how much work was done to compress the gas:
If we plug in the values for , , and for our example, we get:
Let's check the sign for the work to make sure it makes sense. We know the gas had work done on it, since the volume of the gas decreased. That means the value of work we calculated should be positive, which matches our result. Hooray! We can also convert our calculated work to Joules using the conversion factor:
Thus, we did of work to compress the gas in the bicycle pump from to .
Work when volume or pressure is constant
There are a few common scenarios where we might want to calculate work in chemistry class, and it helps to be able to recognize them when they come up. We will discuss how work is calculated for these cases.
Constant volume processes
Sometimes reactions or processes occur in a rigid, sealed container such as a bomb calorimeter. When there is no change in volume possible, it is also not possible for gases to do work because . In these cases, and change in energy for the system must occur in other ways such as heat.
Bench (or stove) top reactions: Constant pressure processes
In chemistry, we will often be interested in changes in energy that occur during a chemical reaction at constant pressure. For example, you may run a reaction in an open beaker on the benchtop. These systems are at constant pressure because the pressure in the system can equilibrate with the atmospheric pressure of the surroundings.
In this situation, the volume of the system can change during the reaction, so and work is also non-zero. Heat can also be transferred between the system (our reaction) and the surroundings, so both work and heat must be considered when thinking about the energy change for the reaction. The energy contribution from work becomes more significant when the reaction makes or consumes gases, especially if the number of moles of gas changes substantially between the product and the reactants.
Other chemical processes result in only a small volume change, such as in the phase change from a liquid to a solid. In these cases, the energy change due to work will also be quite small, and may even be ignored when calculating the energy change. The relationship between work, heat, and other forms of energy transfer is further discussed in the context of the first law of thermodynamics.
Podsumowanie
- Work is the energy required to move something against a force.
- The energy of a system can change due to work and other forms of energy transfer such as heat.
- Gases do expansion or compression work following the equation:
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