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This is because a general process for this case may include work being done on the system by its surroundings, which can have frictional or viscous effects inside the system, because a chemical reaction may be in progress, or because heat transfer actually occurs only irreversibly, driven by a finite difference between the system temperature ({{math|''T''}}) and the temperature of the surroundings ({{math|''T''}}_''surr'').<ref name=":0">Adkins, C.J. (1968/1983), p. 75.</ref><ref name="Munster 45"/> Note that the equality still applies for pure heat flow,<ref name="Schmidt-Rohr 14"> Schmidt-Rohr, K. (2014). "Expansion Work without the External Pressure, and Thermodynamics in Terms of Quasistatic Irreversible Processes" ''J. Chem. Educ.'' '''91''': 402-409.  https://dx.doi.org/10.1021/ed3008704 </ref>

This is because a general process for this case may include work being done on the system by its surroundings, which can have frictional or viscous effects inside the system, because a chemical reaction may be in progress, or because heat transfer actually occurs only irreversibly, driven by a finite difference between the system temperature ({{math|''T''}}) and the temperature of the surroundings ({{math|''T''}}_''surr'').

<ref name=":0">Adkins, C.J. (1968/1983), p. 75.</ref><ref name="Munster 45"/>  

Note that the equality still applies for pure heat flow,

<ref name="Schmidt-Rohr 14"> Schmidt-Rohr, K. (2014). "Expansion Work without the External Pressure, and Thermodynamics in Terms of Quasistatic Irreversible Processes" ''J. Chem. Educ.'' '''91''': 402-409.  https://dx.doi.org/10.1021/ed3008704 </ref>

This is because a general process for this case may include work being done on the system by its surroundings, which can have frictional or viscous effects inside the system, because a chemical reaction may be in progress, or because heat transfer actually occurs only irreversibly, driven by a finite difference between the system temperature () and the temperature of the surroundings (_surr).

This is because a general process for this case may include work being done on the system by its surroundings, which can have frictional or viscous effects inside the system, because a chemical reaction may be in progress, or because heat transfer actually occurs only irreversibly, driven by a finite difference between the system temperature () and the temperature of the surroundings (_surr).

(实际上可能是不改变成分的准静态不可逆性)。数学

: <math>\mathrm dS = \frac{\delta Q}{T} \,\, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \text {(actually possible quasistatic irreversible process without composition change 实际上可能是不改变成分的准静态不可逆性).}</math>

 

 

 

 

 

The German scientist [[Rudolf Clausius]] laid the foundation for the second law of thermodynamics in 1850 by examining the relation between heat transfer and work.{{sfnp|Clausius|1850}} His formulation of the second law, which was published in German in 1854, is known as the ''Clausius statement'':

The German scientist [[Rudolf Clausius]] laid the foundation for the second law of thermodynamics in 1850 by examining the relation between heat transfer and work.{{sfnp|Clausius|1850}} His formulation of the second law, which was published in German in 1854, is known as the ''Clausius statement'':

===Kelvin statements===

===Kelvin statements开尔文描述===

[[William Thomson, 1st Baron Kelvin|Lord Kelvin]] expressed the second law in several wordings.

[[William Thomson, 1st Baron Kelvin|Lord Kelvin]] expressed the second law in several wordings.

===Equivalence of the Clausius and the Kelvin statements===

===Equivalence of the Clausius and the Kelvin statements克劳修斯和开尔文陈述的等价性===

 

[[Image:Deriving Kelvin Statement from Clausius Statement.svg|thumb|Derive Kelvin Statement from Clausius Statement]]

[[Image:Deriving Kelvin Statement from Clausius Statement.svg|thumb|Derive Kelvin Statement from Clausius Statement]]