英文版大学物理 第八章

8-2 Heat and Work Done by Thermodynamic Systems Heat Heat is the energy that is transferred between a system and its environment because of a temperature difference that exists between them.
pi f Because Eint = ν RT , O 2 f f ν R∆T = ν R(T f − Ti ) Then ∆E = Q =
int
i V V
Note that Eint is a function of state only, and ∆Eint is independent of processes, but Q depends on the path. Therefore, this equation holds only for constant-volume process.
f i
∆Eint is independent of processes, for any process
∆Eint
From the first law of thermodynamics, heat transfer in an isobaric process is given by f Q = ∆Eint + W = ν R(T f − Ti ) + p (Vf − Vi)
Chapter 8 The First Law of Thermodynamics 8-1 Changes in Thermodynamic Systems 8-2 Heat and Work Done by Thermodynamic Systems 8-3 The First Law of Thermodynamics 8-4 Some Special Cases of the First law of Thermodynamics 8-5 The Molar Specific Heats of an Ideal Gas 8-6 The Adiabatic Expansion of an Ideal Gas 8-7 Heat Transfer Mechanisms
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2. Constant-pressure processes An isobaric process is one in which the pressure is kept constant. p i f If the volume changes from Vi to Vf p while the pressure of the gas is held W>0 constant p, the work done by the O gas is given by Vi Vf V V W = ∫ pdV = p (Vf − Vi) V
8-4 Some Special Cases of the First law of Thermodynamics Q = ∆Eint + W 1. Constant-volume processes p If V = constant, W = 0. Such a process pf is called an isochoric process, f ∆Eint = Q
Heat is neither released nor absorbed Q=0.
Heat is absorbed by the system from the environment Q>0.
Work Done by Thermodynamic Systems Consider a piston of area A pushed out by the pressure p of the gas contained in the cylinder. The infinitesimal work done by the gas in moving the piston ds is
A
r r dW = F ds = pAds
dW = pdV
p ds
The volume changes from Vi to Vf :
During the change in volume, the pressure and temperature may also change. There are actually many ways to take the gas from state i to state f.
8-1 Changes in Thermodynamic Systems Thermodynamic systems in equilibrium, such as a bottle of hot steam, are described by only a few thermodynamic variables. For a gas these variables are p, V, T, ν (or N). For an ideal gas, pV = νRT= NkT. Assume that ν is fixed, then it is enough to describe the (equilibrium) state on a two-dimensional plot, such as a p−V diagram, a p−T diagram, or a V−T diagram. Thermodynamic process When the surrounding is changed, a system will deviate from equilibrium. After a time τ, the system will reach a new equilibrium state (if exists). We say that the system undergoes a thermodynamic process. The time τ is called relaxation time.
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cycle
8-3 The First Law of Thermodynamics If an amount of heat Q enters a thermodynamic system, it could manifest itself as either an increase in internal energy or a resulting quantity of work performed by the system on the surroundings, or a bit of both. Then Q = ∆Eint + W， Checkpoint 2 ， where ∆Eint is the change in the system’s internal energy, W is the net work done by the system. Note that before this chapter, the term work meant that the work done on a system and is symbolized W. However, in this chapter and the next, we define the work and the symbol W as the work done by a system. If the thermodynamic system undergoes only a differential process, dQ = dEint + dW.
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f f = ν R∆T = ν R(T f − Ti ) 2 2
3. Isothermal processes. Suppose that we allow an ideal gas to expand from an initial volume Vi to a final volume Vf while we keep the temperature T of the gas constant. p i pi T isothermal expansion :Vi <Vf isothermal compression : Vi >Vf pf f For an ideal gas, the internal energy W>0 is the function of temperature, thus O Vf V Vi for an isothermal process ∆Eint = 0 From the first law of thermodynamics, Q = W work done by an ideal gas during an isothermal Vf expansion V ν RT W = ∫ pdV = ∫V dV
p Discussion W = dW = V pdV p ∫ ∫V i Process a i A system can be taken W>0 f f from a given initial state W>0 0 expanded to a given final state by V0 V p an infinite number of h p g processes. Heat may or i i may not be involved, and c c f f in general, the work W W>0 0 and the heat Q will have V 0 p V p different values for different Wnet >0 i i process. Checkpoint 1 f f W<0 0 We say that heat and work 0 V V Thermodynamic are path-dependent quantities compressed
Environment System TS Q TS>TE Q <0 TS =TE Q =0 TS<TE TE Environment System TS TE Environment System TS Q Q >0 TE
Heat is lost by the system to the environment Q<0.
Some quasi-static processes
p i (a) (b) (d) (c) V
(a) constant pressure (isobaric) process; (b) isothermal process; (c) isentropic (adiabatic) process; (d) constant volume (isochoric) process.
Quasi-static process To maintain thermal equilibrium at each step in a thermal process, changes must be made such slowly that the time taken by the thermal process is much longer than relaxation time. Such a process is called quasi-static process, which can be represented as a curve on a p−V diagram, a p−T diagram, or a V−T diagram. Unless we state otherwise, we consider only quasistatic process. Thermodynamics is based on our ability to treat quasi-static process. There are situations (such as free expansion) in which processes occur too fast for equilibrium thermodynamics to apply.