## 7. THE FIRST LAW OF THERMODYNAMICS

Statement of the Principle of Conservation of Energy, including thermal energy.

We have seen how the internal energy U of a system changes when the energies of constituent particles vary. This change in the internal energy can take place in two different ways. The transfer of energy at a microscopic level occurs when two systems are put in thermal contact, such that the particles of both system may suffer collisions between them. In these collisions the particles with more energy (those of the system with higher temperature) release some energy that is gained by the particles with less average energy (belonging to the system with lower temperature). The transfer of energy ends up when the two systems reach the same temperature, i.e., when their particles have the same average energy. The energy transferred is the heat Q.

On the other hand, we have also seen how a gas expanding against a piston makes a work W, at the expenses of its internal energy U. This can be regarded as a macroscopic transfer of energy. Summarizing the two cases, the conservation of energy is stated in the First Law of Thermodynamics in the form

### &U = &Q - &W

where the minus sign is used because the convention is adopted that the work is positive when done by the system and negative when done upon the system.

Some experiences will be carried out to become familiar with this Law in various circumstances. First, we shall consider the expansion of a gas against a movable wall with no heat exchange with the environment. A process in which there is no heat exchange is called adiabatic.

 EXPERIENCE: Adiabatic expansion. By clicking the buton we have a gas with a certain energy, confined by a piston that becomes free by pressing "On". Then, the "disordered" energy of the gas is converted through the collisions of the particles with the wall into kinetic energy of the piston, as it is described in Section Pressure, and the gas makes a certain amount of work.  The values of pressure and volume can be seen in a window during the process, in a typical P-V diagram. 07.Q1. QUESTION: In an adiabatic experience such as that described above, The temperature of the gas increases. The internal energy of the system remains unchanged. The change in the internal energy equals the work done by the gas.
On the other hand, if energy is supplied to the gas to exactly compensate the energy given to the piston in each collision then the temperature of the gas will not change. This type of process is called isothermal.

 EXPERIENCE: Isothermal expansion. Press the button "Isothermal" in the control window. Each time a particle collides with the piston the energy loosed by it is released again to the particle so the system does not change their internal energy neither his temperature. 07.Q2. QUESTION: In an isothermal expansion, The internal energy of the system does not change. The change in the internal energy equals to work done by the gas. The heat supplied to the system is larger than the work done by the gas.
The curve corresponding to an isothermal expansions in the P-V diagram is a branch of an hyperbola, as the product of P and V is constant. It is not so in the adiabatic expansion.

WORK IN AN ISOTHERMAL PROCESS

From the state equation of an ideal gas introduced in Section 3 TEMPERATURE, the work done by an ideal gas during an isothermal expansion is given by

where n is the number of moles, and the modified constant appearing in this equation is known as R, the constant of ideal gases.

Entropy

 Index 1.Introduction 2.Pressure 3.Temperature 4.internal Energy 5.Heat 6.Work 8.Entropy 9.Velocity Distribution 10.Specific Heat