Thermodynamics part III. a.) Fenomenological thermodynamics macroscopic description b.) Molecular thermodynamics microscopic description b1.) kinetical gas theory b2.) statistical thermodynamics
Laws of thermodynamics
Basics types of thermodynamical systems 1. Isolated system: The system is thermodynamically isolated if there is no particle and energy exchange between the system itself and its neighbor (or surroundings). Icon: 2. Closed system: The system is thermodynamically closed if there is no particle exchange (but there might be energy exchange) between the system and its surroundings. Icon: 3. Opened system: The system is thermodynamically open if there might be particle and energy exchange between the system and its surroundings. Icon:
Work done by the outer system on its surroundings 1. Work elements: Work belongs to the change of the volume: W i = p i dv i i = 1, 2,, n n N 1. Total work done by the outer system on the gas system: n W = p i dv i 2. Using infinitesimally short divisions for definition of the total work: V 2p W = dv 3. Work done by the gas on the outer system or surroundings: i=1 V 1 W = W = V 2p dv V 1
Work done by the outer system on its surroundings p p 1 1. p 2 W 2. V 1 V 2 V Magnitude of the work done by the gas on the surroundings is equal to the numerical value of the area under the plot.
Internal energy of the ideal gas (U) Definition of the internal energy for the ideal gas is based on the energy types associated with the gas system. An ideal gas system has two types of energies: 1. Kinetical energy 2. Potential energy Consequently: Inertial energy of the ideal gas = Sum of (Kinetical energy + potential energy) Symbol: U Dimension: joule, J
First law of thermodynamics conservation of energy 1. Macroscopic form: U = Q + W 2. In words: The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic systems. The law of conservation of energy states that the total energy of an isolated system is constant; energy can be transformed from one form to another, but cannot be created or destroyed. The first law of thermodynamics recognizes a particular form of energy called internal energy. It is often formulated by stating that the change in the internal energy of a closed system is equal to the amount of heat supplied to the system, plus the amount of work derived to the system. It is also often formulated by stating that when a closed system has a change of state, and its internal energy is changed only by work and not by heat transfer, then the net amount of work transferred is the same for all arrangements of work transfer that are possible for that change of state. Also, when two systems, open to each other for transfer of matter and energy, interact but are otherwise isolated, then the sum of their internal energies does not change. 1. Microscopic form: du = δq + δw
Processes for ideal gases I. Isochoric process (V=constant) V = constant dv = 0 But: dw = p dv = 0 Form of the first law of thermodynamics in this case: du = δq + δw = δq + 0 = δq But: Q = c V m T δq = c V m dt du = δq (after integration) U = Q So: U = c V m T U = c V m T
Processes for ideal gases II. Isobar process (p=constant) p = constant Heat element: δq = c p m dt Q = c p m T Work done by the surroundings on the gas: W = p dv Definition (enthalpy): It is a status indicator and defined by the following way: H = U + pv Form of the first law of thermodynamics: property of derivation: du = δq + δw du δw = δq du p dv = δq du + p δw = δq d U + pv = δq dh = δq dh = c p m dt H = c p m T
Processes for ideal gas III. Isotherm process (T=constant) T = constant Internal energy of the ideal gas: du = 0 U = 0 Form of the first law of thermodynamics: du = δq + δw = 0 or δq = δw = p dv The work done by the surroundings on the gas: W = m M RT ln V later V earlier = m M RT ln V 2 V 1 The heat: Q = W = + m M RT ln V later V earlier = + m M RT ln V 2 V 1
Processes for ideal gases IV. Adiabatic process (Q=0) Definition (adiabatic process): There is no heat exchange between the gas system and its surroundings: Q = 0 Form of the first law of thermodynamics: du = δq + δw or du = 0 + δw = δw For macroscopic quantities: U = W = c V m T More formulas for adiabatic processes: Ratio of the heat capacities: κ = c p c V = C p C V T V κ 1 = constant T 1 V 1 κ 1 = T 2 V 2 κ 1 Poisson formula: p V κ = constant p 1 V 1 κ = p 2 V 2 κ T κ p κ 1 = constant T 1 p κ 1 = T 2 1 κ κ p 2 κ 1
Processes: p=const p isobar isotherm isochoric adiabatic V=const V