Chapter XV The First Law of Thermodynamics

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Chapter XV The First Law of Thermodynamics

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 We knew that the concepts of mechanical work and energy play an important role in studying mechanical phenomena.  Concerning to thermal phenomena, there exits a new form of energy called “heat”: Heat can be transferred from one to other systems For a system with volume held constant, the effect of heat is to change the temparature of a system.

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  1. GENERAL PHYSICS II Electromagnetism & Thermal Physics 4/29/2008 1
  2. Chapter XV The First Law of Thermodynamics §1. Heat, work and paths of a thermodynamic process §2. The first law of thermodynamics §3. Kinds of thermodynamic processes §4. Thermodynamic processes for an ideal gas 4/29/2008 2
  3.  We knew that the concepts of mechanical work and energy play an important role in studying mechanical phenomena.  Concerning to thermal phenomena, there exits a new form of energy called “heat”: Heat can be transferred from one to other systems For a system with volume held constant, the effect of heat is to change the temparature of a system. In general cases, for a system there exist, at the same time, transfer or exchange of heat and mechanical work → the GOAL of thermodynamics is the study of the relationships involving heat, mechanical work, the laws that govern energy transfers 4/29/2008 3
  4. §1. Thermodynamic systems and processes: 1.1 Thermodynamic systems, heat and work:  In any study of heat, work transfer we must define exactly what are the objects under consideration: A thermodynamic system is any collection of objects that is regarded as a unit and that may have the potential to exchange energy with other bodies beside the system All the other bodies which have energy exchanges with the considered system are called surroundings or environment 4/29/2008 4
  5. surroundings  Then we must fix the convention on the symbol for heat and work: system We will always denote Q>0  by Q the quantity of heat added to the system  by W the mechanical work done by the system Therefore Q and W are understood as algebraic surroundings values, they can be positive, negative or zero. system surroundings surroundings Q0 W
  6. 1.2 Calculation of work done during volume changes:  A typical example of a thermodynamic system is an amount of gas enclosed in a cylinder with a movable piston. (Such a system is the central part of heat engines: locomotive, engine of a car, refrigerator,…).  When a gas expands, it does work on its dx A environment. For a small displacement dx, the work done by the gas is: dWby = F dx = p A dx = p (A dx)= p dV  Consider the expansion of gas of from an initial state (with the volume V1 ) to a final state (the volume V2). The system (gas) passes through a series of intermediate states. We assume the changes of states are slow enough, then every intermediate state can establish equilibrium, and has determined values of p, V, T. 4/29/2008 6
  7.  The work done by the gas during the whole change V1 → V2 is V2 W by  pdV V1 Note that when the gas expands, V2 > V1 → Wby > 0 , and when the gas is compressed, V2 < V1 → Wby < 0 (it means that the surroundings does work on the gas).  In a p-V diagram, the equilibrium intermediate states are represented by the points on a curve, and the work is represented as the area under the curve p V1 V2 V 4/29/2008 7
  8. 1.3 Paths between thermodynamic states:  When a thermodynamic system changes from an initial state to a final state, it passes through a series of (equilibrium) intermediate states. However, with the same initial and final states, the system can pass in very different ways. On a P-V diagram, every way corresponds to a curve which is called the path between thermodynamic states.  Examples: Two different paths between the states 1 and 2 : p p 1 1 p1 3 p1 p2 4 2 p2 2 V2 V V V1 1 → 3 : keep the pressure constant 1 → 4: reduce the pressure at p1 while the gas expands at the constant volume V1 to the volume V 2 4 → 2: keep the pressure 3 → 2 : reduce the pressure to p2 at constant at p2 while the gas constant volume V2 expands to the volume V2 4/29/2008 8
  9.  It is important to remark that with the same intial and final states:  The work done by the system depends on the intermediate states, that is, on the path,  Like work, the heat which the system exchanges with the surroundings depends also on the path. Examples: p 1 p 1 2 2 V V In an isothermal expansion of the gas Gas can expand in an we must supply an input heat to keep container which is isolated constant temperature from surroundings (no heat input) 4/29/2008 9
  10. §2. The first law of thermodynamics: 2.1 Internal energy of a system:  The internal energy of a system is the energy that the system owns. We can define: Internal energy = ∑kinetic energies of constituent particles + ∑potential energies between them (Note that the internal energy does not include potential energy arising from the interaction between the system and its surroundings, for example, system and gravitaitonal field).  For an ideal gas we know how can calculate the internal energy. But for any real system, the calculation of the internal energies by this way would be very complicated. 4/29/2008 10
  11.  We have another way. Practically, in the study of thermodynamical processes, we can determine not just the interal energy U , but the change in internal energy Δ .U We can choose by convention the internal energy of the system at any reference state, and then knowing Δ we can determine U U at all other states. (Recall that the potential energy of a particle in a gravitational field, or the potential energy of a charge in the static electric field are defined with the precision to an adding constant). Having the concept of the internal energy, we can formulate the first law of thermodynamics 4/29/2008 11
  12. 2.2 Formulation of the first law of thermodynamics:  Consider a change of state of the system from an initial value U1 to a final value U 2 , then Δ = U2 – U1 . U If the change is due to the addition of a quantity of heat Q with no work done → the inernal energy increases, and Δ = Q . U If the system does work W by expanding and no heat is added, the internal energy decreases, we have Δ = - W U  The first law of thermodynamics states that when both heat transfer and work occur, the total change in internal energy is Δ =Q-W U Note: Always remember the convention on the signs of Q and W 4/29/2008 given before !!! 12
  13. §3. Kinds of thermodynamic processes: We know that there are many different paths between thermodynamic states. We will study four specific kinds of thermodynamic processes which are important in practical applications. 3.1 Adiabatic process: 1 2  Definition: Adiabatic process is defined as p one with no heat transfer into or out of a system, Q = 0.  Examples: V Gas in a container which is surrounded by a thermally isolating material A expansion (or compression) of gas which takes place so quickly that there is not enough time for heat transfer.  From the 1st law: Δ = U2 – U1 = - W U (adiabatic process) 4/29/2008 13
  14. 3.2 Isochoric process:  Definition: This is a constant-volume process.  Example: A gas in a closed constant-volume 2 container. p  When the volume of a thermodynamic system is 1 constant, it does no work on its surroundings W=0 V  From the 1st law: Δ = U2 – U1 = Q U (isochoric process)  Since the system does no work → all the energy (heat) added remains in the system → the iternal energy increases. 4/29/2008 14
  15. 3.3 Isobaric process: 1 2  Definition: This is a constant-pressure process. p  In a isobaric process, none of three quantities Δ Q, W is zero. U, V  Work done by the system is easily calculated: W = p (V2 – V1 ) 4/29/2008 15
  16. 3.4 Isothermal process: 1  Definition: This is a constant-temperature 2 p process  To keep temprature constant, the system must exchange heat with the surroundings, and the V exchange must be slowly that thermal equilibrium is maintained.  In general, in a isothermal process, none of Δ Q, W is zero U,  Only in the case of an ideal gas, the internal energy U ~ T → Δ = 0 in a isothermal process. U 4/29/2008 16
  17. §4. Thermodynamic processes for an ideal gas:  In this section, by applying the 1st law of thermodynamics we study in more details thermodynamic processes for an ideal gas.  For an ideal gas, with the help of kinetic-molecular model, we know that the internal energy of an ideal gas depends only on its temperature, not on its pressure or volume.  Owing to the explicit relation between the internal energy U and temperature T we can find explicit equations which relate heat, work and internal energy. 4/29/2008 17
  18. 4.1 Constant-volume and constant-pressure heat capacities of an ideal gas:  We knew the concept of heat capacity of an ideal gas in a constant-volume process. Now consider more general cases of thermodynamic process.  The general definition of heat capacity is the following equation: where Δ is the quantity of heat added to the system for increase Q Δ in temperature. T This definition can give rise different heat capacities which depend on the paths of thermodynamic process. 4/29/2008 18
  19.  The constant-volume heat capacity is defined by Notes:  Here we replace Δ by Δ because no work done in the process Q U  If we understand CV as molar constant-volume heat capacity, then Δ is the heat added per mole Q  The constant-pressure heat capacity: For a constant-pressure process the effect of the heat added to the system is twofold: to increase the internal energy and to do work 4/29/2008 19
  20. • Applying the 1st law we can write • At the limit Δ → 0 : T • In the case of an ideal gas, U depends only on T , we have • Using the equation of state of an ideal gas we obtain the relation for the molar heat capacities CP and CV : CP = CV + R (See experimantal values of CV and CP given in textbook, p. 740, tab. 19.1) 4/29/2008 20

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