Peter's Physics Pages

A Semester of First Year Physics with Peter Eyland

Lecture 6 (First Law of Thermodynamics)

In this lecture the following are introduced:
• Equilbrium Thermodynamics
• The Work Done by a system
• Cyclic processes
• The First Law of Thermodynamics
• Constant Volume changes
• Cyclic changes
• Free Expansions

Equilibrium Thermodynamics

Thermodynamic equilibrium occurs in a system when
• the resultant force is zero throughout the system,
• the temperature is constant throughout the system, and
• the internal structure and chemistry do not change.
When one or more of these variables change, then the system is said to undergo a change of state (which must be distinguished from a change of phase: solid <->liquid <-> gas).

In equilibrium thermodynamics any change of state that takes place is performed very, very, slowly. This is to keep the system always infinitesimally near an equilibrium state. Such changes are called quasi-static processes, (which is the change you have when you don't have a change!). In what follows quasi-static processes are assumed unless indicated otherwise.

The Work Done by a system in changing volume

External work is done on or by a system, when the system as a whole exerts a force on its surroundings and produces a displacement. Only external work is considered here. For example, a gas confined to a cylinder can expand its volume by displacing a piston. Take the situation where an insulated cylinder has a piston weighed down by a container of Lead shot, and a base that has a heat source, which can change the temperature of the system. The system in the diagram is initially in equilibrium. A tiny amount of Lead shot is removed and the reduced weight provides a small constant force, F, to move the piston a small distance, ds. The differential work done by the system is: where p is the small constant pressure and dV is the differential volume change. Since the Joule is a work or energy unit, the product of pressure times volume gives a quantity of work. When the volume increases from an initial volume, Vi, to a final volume, Vf, the work done by the system is the area under the p vs V curve:  The work done by the system is positive because the volume has increased. In evaluating the work done by the system, the actual way that the pressure changes will determine the result.

Case 1: The first change, from "i", to "a", occurs at constant pressure (an isobaric change).

To increase the volume at constant pressure, the temperature has to be turned up by adding heat (+Q1) while the piston is allowed to move freely against the weight.
The second change, from "a", to "f", occurs at constant volume (an isochoric change).

To decrease the pressure at constant volume, the piston has to be fixed in place and the temperature turned down by subtracting heat ( -Q2).

Case 2: The first change is at constant volume: the piston fixed in place and the temperature reduced.
The second change is at constant pressure: the piston is free and the temperature increased.

Considering the work done by the system in each case: The system moves from identical initial states to identical final states. The work done by the system is larger along the first path than the second (as see by the coloured areas). The work can be made as small as you like or as large as you like by choosing a suitable path. Example
A sample of gas expands from 1 m3 to 4 m3 while its pressure decreases from 30 kPa to 10 kPa as shown in the diagram. Find the work done by the gas along each of the three paths "abc", "adc", and diagonally "ad".  Cyclic Processes

Since the work done by the system and the heat added to the system are dependent on the path taken, there will be net work done by the system in cycling around a closed path as shown below. Example
Find the net work done by a gas around the cycle "abca" shown in the diagram.  The First Law of Thermodynamics

From the diagrams above, the work done by the system and the heat added to the system vary with the path taken. However the difference between the heat added and the work done by the system is the same for all paths. Tise constant difference represents the change in internal energy between the two states.
The first law of thermodynamics says that when a system changes from one state to another, the change in internal energy equals the heat added to the system minus the work done by the system.
In symbolic form: Note that a body does not "contain heat" or "contain work". Heat and work are energy in transition that changes the internal energy. When heat is added to the system the internal energy increases. When work is done by the system the internal energy decreases.

Example
A thermodynamic system is taken around the cycle "abca" shown in the diagram. Complete the following table. Q W ΔU ab bc +ve ca -ve

When you have tried to answer this question for yourself, scroll down for the completed answer in the following table.

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 Q W ΔU ab cool (-ve) 0 -ve bc heat (+ve) +30 kJ +ve ca cool (-ve) -60 kJ -ve

Special Cases

In an adiabatic change there is no heat transfer between the system and its surroundings. From the First Law: When no heat is transferred, • work done by the system decreases the internal energy so the temperature drops, and • work done on the system increases the internal energy so the temperature rises.

One way of ensuring an adiabatic change is to carry it out rapidly. This happens with sound waves and internal combustion engines.

Constant Volume changes

Since the volume doesn't change no work is done.
From the First Law: Heat added to the system increases the internal energy. Heat removed from the system decreases the internal energy.

Cyclic Changes

In a cyclic process the system returns to its initial state and so the internal energy is not changed.
From the First Law: The heat added to the system equals the work done by the system.

Free Expansions
A free expansion is an adiabatic change that does no work. From the First Law: From the diagram, the insulation means no heat transfer and there is no change in the volume of the system.

As the name implies a free expansion is not a quasi-static process, it can only happen rapidly and we cannot describe it on a p vs V diagram.

Example
A gas undergoes a cyclic change "abca" as shown in the diagram. 20 J of heat are added from a to b; b to c is an adiabatic change; and the net work done by the system is 15 J. Find the heat added to the system in changing from c to a.  Summarising:

In equilibrium thermodynamics any change of state is performed quasi-statically.

 The work done by a system is the area under the p vs V curve  There will be net work done by taking a system around a closed path since work and heat are path dependent.
The 1st Law of Thermodynamics: When a system changes from one state to another, the change in internal energy is the heat added to the system less the work done by the system. In symbols: In an adiabatic change there is no heat transfer between the system and its surroundings.
In a constant volume change the heat added to the system increases the internal energy and vice versa.
In a cyclic process the system returns to its initial state and so the internal energy is not changed.
A free expansion is an adiabatic change that does no work. email Write me a note if you found this useful

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