15.2 The First Law of Thermodynamics and Some Simple Processes
The heat is transferred because of the temperature difference.
Characterized by random motion.
Energy is transferred by a force.
An orderly process.
The Industrial Revolution harnessed power through the use of the first law of thermodynamics.
61 years after the first explicit statement of the first law of thermodynamics was made, this photo of a steam engine at the Turbinia Works was taken.
The most important thing we can do with heat transfer is to use it for work.
There are examples of heat engines.
The first law of thermodynamics governs the representation of a heat engine.
It is not possible to design a system where no heat transfer occurs to the environment.
When the gas expands, the pressure and temperature fall, indicating that the gas's internal energy has been decreased.
One of the ways in which heat transfer works is shown in the illustrations above.
Fuel combustion increases the pressure of the gas in the cylinder and the force it exerts on the piston.
The gas works on the outside world, as the force moves the piston through some distance.
Work is being done when heat is transferred to the gas cylinder.
To do this again, the piston needs to be returned to its starting point.
A force is put on the surroundings to push the piston back through some distance in order to decrease the pressure on the gas.
Hundreds of millions of heat engines use variations of this process daily.
In the next section, we will look at heat engines.
Some of the simpler underlying processes on which heat engines are based are considered in this section.
An isobaric expansion of a gas requires heat transfer.
The work done is constant.
Positive means that work is done by the gas on the outside world.
The work done would be anisobaric process if we called the pressure outside the tank.
This definition of work is used by many texts as the basis of the first law of thermodynamics.
Since we have already noted in our treatment of fluids that pressure is a type of potential energy per unit volume and that pressure in fact has units of energy divided by volume, it is not surprising.
The ideal gas law has units of energy.
Some of the energy associated with pressure becomes work.
A diagram for an isobaric process is shown in Figure 15.10 The area under the graph is shown in the figure.
A graph of pressure versus volume for a constant-pressure, or isobaric, process, such as the one shown in area under the curve equals the work done by the gas, since
The area under the curve over that interval is the average pressure times the change in volume.
The total work done is equal to the total area under the curve.
This is thought to be a negative area under the curve.
Figure 15.11(a) shows a more general process in which both pressure and volume change.
The area under the curve is closely approximated by dividing it into strips, each having an average constant pressure.
The total work done is the sum of the work done for each strip.
The area under the curve is the total work done.
The area under the curve is negative.
No work is done in an isochoric process since volume is constant.
The negative area below path CD subtracts from the area inside the rectangle.
Figure 15.12(c) shows a general process.
For work to be positive, it must be done in the clockwise direction.
The path ABC is at higher pressure than the path ADC.
The area under the path is where the work is done.
This area is better for path ABC.
It is work done on the outside environment if the loop is in a clockwise direction.
It is work that is done to the system if the loop is traveled in a counter-clockwise direction.
You can find the work along any path on a diagram if you know the pressure times change in volume.
The value is calculated for each leg of the path.
The path BC is isochoric.
The work along path CD is negative.
Since the path is isochoric.
The area inside the closed loop is the same as the work done outside.
The area is easier to calculate than the work done on each path.
To see which processes produce the most work, it's a good idea to see the area inside the curves on diagrams.
Work can be done to the system, or by the system, depending on the sign.
A positive is work done by the system on the outside environment while a negative is work done by the environment on the system.
Two important processes are shown in Figure 15.13(a).
Both are shown at the same point.
If the gas behaves like an ideal gas and no phase change occurs, then.
It is a constant for an isothermal process.
We assume that heat transfer must occur from the surroundings to the gas to keep the temperature constant during an isothermal expansion.
The internal energy of an ideal monatomic gas is constant during an isothermal process.
The net heat transfer into the gas must equal the net work done by the gas if the internal energy doesn't change.
We need enough heat transfer to replace the work done.
An isothermal process takes a long time because heat transfer occurs continuously to keep the gas temperature constant, and must be allowed to spread through the gas so that there are no hot or cold regions.
It is possible to achieve processes that are nearly adiabatic by using very effective insulation or by performing the process so fast that there is little time for heat transfer.
Less work is done because curve AC is lower than curveAB because of lower temperature.
If the path ABCA could be followed by cooling the gas from B to C at constant volume, there would be a net work output.
The isothermal process works better than the adiabatic because heat transfer into the gas keeps its temperature constant.
The isothermal path keeps the pressure higher than the adiabatic path.
Even though the final volume is the same as for the isothermal process, the adiabatic path ends up with a lower pressure and temperature at point C.
Both the reverse isothermal and adiabatic paths are called BA and CA.