Thermodynamics Quiz: Internal Energy of Gases

Lecture 9 Summary

• Lecture 9 covers internal energy, thermodynamic systems, the zeroth law of thermodynamics, and the first law of thermodynamics.

• The reading material is from Cutnell & Johnson sections 14.3, 15.1-15.3.

• Internal energy (U) is the sum of all the energies of the individual atoms or molecules of a substance. This includes translational, rotational, vibrational (kinetic and potential) energies, and potentially other energies (e.g., magnetic).

• For a monatomic gas, atoms are considered point-like with mass concentrated at the point. There is no rotational, vibrational, or chemical bonding energy. Internal energy is the sum of only the translational kinetic energies.

• For N particles, U = N * (1/2) * mv_rms². Using the microscopic definition of temperature, mv_rms²/2 = (3/2)kT, internal energy becomes U = N * (3/2)kT. n moles can replace N particles, so U = (3/2)*nRT.

• Internal energy is proportional to Kelvin temperature for any ideal gas, although the constant of proportionality can differ based on the gas type (monatomic, diatomic, etc.)

• Thermodynamics is the branch of physics dealing with heat and its relation to other energy forms and work. It looks at macroscopic properties like temperature, internal energy, pressure, and volume.

• A car engine is an example of a thermodynamic system: Fuel is burned at high temperatures. Some internal energy is used to drive pistons, and excess heat is removed by the cooling system.

• A thermodynamic system is the object or collection of objects of interest. Surroundings are everything else in the environment.

• Heat and work may transfer between the system and the surroundings.

• Walls of a system, like diathermal walls, permit heat flow, or adiabatic walls (perfectly insulating) prevent heat flow.

• The zeroth law of thermodynamics states: Two systems individually in equilibrium with a third system are in thermal equilibrium with each other. This signifies a shared temperature. No heat flow occurs between objects of the same temperature in contact. Thermal equilibrium exists when there's no heat flow between two objects when brought in contact. Temperature is the indicator of this equilibrium.

• The zeroth law of thermodynamics is useful conceptually in defining a temperature scale in relation to various objects and systems. For example, a thermometer is used as a third system to determine if two other systems are in thermal equilibrium with each other.

• First law of thermodynamics: Forces can do work, changing the kinetic and potential energy of an object. A substance's atoms/molecules collide; exert forces on each other and surrounding walls. This gives kinetic and potential energy. Internal energy is the total sum of this energy and other molecular energies.

• When heat or work occurs in a thermodynamic system, the internal energy can change as a result. The first law relates the change in internal energy to the heat transferred and the work done.

  • AU = U_f – U_i = Q – W
  • A system gains heat (Q), the change in internal energy (AU) is equal to the heat gained minus the work done. The sign convention is that heat is positive when the system gains heat, and negative when it loses heat. Work (W) is positive when done by the system and negative when done on the system.

• The example problems illustrate how heat and work affect the change in internal energy (AU) of a system (following the first law in either scenario with heat being absorbed by the system, or work done by the system or on the system.