Thermal contact

1. Thermal contact Two systems are in thermal (diathermic) contact, if they can exchange energy without performing macroscopic work. This form of energy transfer (random work) is called heat.

2. Mechanisms of Heat Transfer 1. Thermal Conduction law of thermal conduction: A dx

3. Mechanisms of Heat Transfer 1. Convection natural convection: resulting from differences in density forced convection: the substance is forced to move by a fan or a pump. The rate of heat transfer is directly related to the rate of flow of the substance. dQ = cTdm

4. B E Mechanisms of Heat Transfer 1. Radiation Energy is transmitted in the form of electromagnetic radiation. Stefan’s Law  = 6  10-8 W/m2K A – area of the source surface e – emissivity of the substance T – temperature of the source

5. Zeroth law of thermodynamics Thermal Equilibrium: If the systems in diathermic contact do not exchange energy (on the average), we say that they are in thermal equilibrium. If both systems, A and B, are in thermal equilibrium with a third system, C, then A and B are in thermal equilibrium with each other.

6. h Temperature We say that two systems in thermal equilibrium have the same temperature. (Temperature is a macroscopic scalar quantity uniquely assigned to the state of the system.) Gas Thermometer T3 = 273.16 K is the temperature at which water remains in thermal equilibrium in three phases (solid, liquid, gas). The Celsius scale and, in the US, the Fahrenheit scale are often used. ;

7. dl l D dD Thermal expansion For all substances, changing the temperature of a body while maintaining the same stress in the body causes a change in the size of the body. linear expansion: dl = ldl The proportionality coefficient (T) is called the linear thermal expansion coefficient. volume expansion: dV =VdV The proportionality coefficient (T) is called the volume thermal expansion coefficient.

8. The differential amount of absorbed heat (dQ), necessary to change the temperature of the system, is proportional to the change in temperature (dT) of the system. Heat Capacity The proportionality coefficient C is called the heat capacity of the system. If heat capacity does not depend on temperature: Q = C  T

9. The heat capacity of a system in proportional to the amount of matter in the system and depends on the material of the system. specific heat and molar heat capacity If the amount of matter is expressed by mass (m): C = c  m where c is called specific heat If the amount of matter is expressed by the number of moles (n), C = Cm n where Cm is called molar heat capacity

10. specific heat 600 K temperature temperature dependency of heat capacity The specific heat of lead (at atmospheric pressure) The heat capacity of a system depends on the thermodynamic process and the temperature of the system. 128 (J/kgK)

11. At (first type) phase transitions, the amount of absorbed heat is proportional to the amount of transformed substance Q = L  m Latent Heat The proportionality coefficient is called latent heat.

12. T V P Thermodynamic Process Macroscopically, the state of a system of particles is described by uniquely assigned parameters. A thermodynamic process is a sequence of states of the system. In a thermodynamic process the state parameters are functions of time.

13. internal energy in common processes • adiabatic process- no heat is transferredU = W (dU = -dW) • isochoric process- constant volume processU = Q (dU = dQ) • cyclical process- the system returns to the initial stateU = 0 • isothermal process- constant temperatureU = Q - W (dU = dQ - dW) (for an ideal gas dU = 0) • isobaric process- constant pressureU = Q - W (dU = dQ - dW) • free expansion- adiabatic with no work doneU = 0 (dU = 0)

14. Ideal Gas macroscopic definition: An ideal gas is one that obeys the equation of state PV = nRT P - pressure n - amount (in moles) V - volume R - universal gas constant T - temperature microscopic definition: Except for elastic collisions the particles of an ideal gas do not interacts - the range of interaction is very short.

15. pressure volume Isothermal process in an ideal gas (Boyle‑Mariotte law) The temperature of the system (an ideal gas) is kept constant. < T3 T1< T2

16. volume temperature Isobaric process in an ideal gas (Charles and Gay-Lussac law ) The pressure of the system is kept constant. P3 < P2< P1

17. pressure temperature Isochoric process in an ideal gas The volume of the system is kept constant. V3 < V2< V1

18. (integral form ) Macroscopic Work When the volume of the system changes, the system performs (macroscopic) work. dx Work depends on the thermodynamic process!

19. a b P V T First law of thermodynamics For each thermodynamic process, the difference between heat delivered to the system and the work done by the system depends only on the initial and the final state of the system. There is such a function state U, called internal energy, that dU = dQ - dW where dQ is the heat delivered to the system and dW is the work performed by the system. Comment: On the microscopic scale, the internal energy of a system is the total mechanical energy of the system.

20. Internal energy of an ideal gas The internal energy of an ideal gas results from the translational kinetic energy, rotational kinetic energy, and vibrational energy of the molecules constituting the system. According to the kinetic theory of gases, the internal energy of an ideal gas is a function of temperature only U = nCVT proof. From the first law of thermodynamics dU = dQ = nCVdT With the reference for the internal energy at 0 K:

21. a b P V T Entropy For any cyclical quasi-static process (The change in entropy from the initial state to the final state does not depend on the process.) We can introduce a function S, called entropy, that is a function of state of the system.

22. The change in entropy between two equilibrium states is given by the heat transferred, dQr, in a quasi-static process leading from the initial to the final statedivided by the absolute temperature, T, of the system definition of entropy macroscopic: microscopic: If the number of possible configurations for a considered state of a system is W (statistical sum), the entropy S of the system in this state is S  kB ln W where kB is a physical constant (Boltzmann’s constant).

23. Second law of thermodynamics In any thermodynamic process that proceeds from one equilibrium state to another, the total entropy of the system and its environment (the Universe) cannot decrease.

24. It is impossible to construct a heat engine which when operating in a cycle, produces no other effect than the absorption of thermal energy from a reservoir and the performance of an equal amount of work Th Qh W Qc Tc engine consequences of the second law of thermodynamics If it was possible With the heat sink engine efficiency

25. It is impossible to transfer heat from one body to another body at a higher temperature with no other consequences in the universe. consequences of the second law of thermodynamics The change in entropy: T1 T2 from which dQ

26. Reversible and irreversible processes If, during a thermodynamic process, the entropy of the Universe is not changed, the process is reversible. If during a thermodynamic process the entropy of the Universe is changed (increased), the process is irreversible.

27. Molar heat capacity of an ideal gas in an isobaric process is related to the molar heal capacity in an isochoric process by Gas Constant(molar heat capacity of an ideal gas) in an isobaric process: dU = dQ - dW = nCPdT - nRdT nCVdT = PV = nRT PdV = nRdT CP = CV + R

28. Adiabatic process in an ideal gas dU = -dW = -PdV (no heat) nCVdT = (for ideal gas) PdV + VdP = nRdT (eliminating temperature)

29. P D A Qh B Th Qc C Tc V Qc Tc Qh Th The Carnot cycle adiabatic expantion isothermal expantion isothermal compression adiabatic compression The work W done by the gas equals the net heat delivered to the gas in the cycle W = Qh - Qc

30. D P C B Qc Qh O A W V2 V1 V four-stroke combustion engine(Otto cycle) The Otto cycle represents operation of a common gasoline engine. The cycle includes two isobaric, two isochoric and two adiabatic processes. 1. intake 2. compression 3. work 4. exhaust

31. Th Qh Qc Tc W engine Refrigerators A refrigerator is a device that moves heat from a system at a lower temperature to the system with higher temperature. The effectiveness of a refrigerator is described in terms of the coefficient of performance The highest possible coefficient of performance is that of a refrigerator whose working substance is carried through a reverse Carnot cycle