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An equilibrium state Surface of equation of state
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Fig. 1.1 Geometrical representation of the
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equation of state.
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thermodynamics a state automatically means a state in equilibrium unless otherwise specified. A thermodynamic transformation is a change of state. If the initial state (f) is an equilibrium state, the transformation can be brought about only by changes in the external condition of the system. The transformation is quasi-static if the external condition changes so slowly that at any moment the system is approximately in equilibrium. It is reversible if the transformation retraces its history in time when the external condition retraces its history in time. A reversible transformation is quasi-static, but the converge is not necessarily true. For example, a gas that freely expands into successive infinitesimal volume elements undergoes a quasi-static transformation but not a reversible one. (g) The P- V diagram of a system is the projection of the surface of the equation of state onto the P- V plane. Every point on the P- V diagram therefore represents an equilibrium state. A reversible transformation is a continuous path on the P- V diagram. Reversible transformations of specific types give rise to paths with specific names, such as isotherms, adiabatics, etc. A transformation that is not reversible cannot be so represented. (h) The concept of work is taken over from mechanics. For example, for a system whose parameters are P, V, and T, the work dW done by a system in an infinitesimal transformation in which the volume increases by dV is given by dW=PdV (i) Heat is what is absorbed by a homogeneous system if its temperature increases while no work is done. If !1Q is a small amount of the heat absorbed, and !1T is the small change in temperature accompanying the absorption of heat, the heat capacity C is defined by !1Q = C!1T The heat capacity depends on the detailed nature of the system and is given as a part of the specification of the system. It is an experimental fact that, for the same !1T, !1Q is different for different ways of heating
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up the system. Correspondingly, the heat capacity depends on the manner of heating. Commonly considered heat capacities are C v and Cp , which respectively correspond to heating at constants V and P. Heat capacities per unit mass or per mole of a substance are called
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(j) specific heats. A heat reservoir, or simply reservoir, is a system so large that the gain
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or loss of any finite amount of heat does not change its temperature. (k) A system is thermally isolated if no heat exchange can take place between it and the external world. Thermal isolation may be achieved by surrounding a system with an adiabatic wall. Any transformation the system can undergo in thermal isolation is said to take place adiabatically. (I) A thermodynamic quantity is said to be extensive if it is proportional to the amount of substance in the system under consideration and is said to be intensive if it is independent of the amount of substance in the system under consideration. It is an important empirical fact that to a good approximation thermodynamic quantities are either extensive or intensive. (m) The ideal gas is an important idealized thermodynamic system. Experimentally all gases behave in a universal way when they are sufficiently dilute. The ideal gas is an idealization of this limiting behavior. The parameters for an ideal gas are pressure P, volume V, temperature T, and number of molecules N. The equation of state is given by Boyle's law: PV - = constant (for constant temperature)
The value of this constant depends on the experimental scale of temperature used. The equation of state of an ideal gas in fact defines a temperature scale, the ideal-gas temperature T:
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k = 1.38 x 10 -16 erg/deg
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which is called Boltzmann's constant. Its value is determined by the conventional choice of temperature intervals, namely, the Centigrade degree. This scale has a universal character because the ideal gas has a universal character. The origin T = 0 is here arbitrarily chosen. Later we see that it actually has an absolute meaning according to the second law of thermodynamics. To construct the ideal-gas temperature scale we may proceed as follows. Measure PV/Nk of an ideal gas at the temperature at which water boils and at
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