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The second law of thermodynamics is a physical law based on universal empirical observation concerning heat and energy interconversions. A simple statement of the law is that heat always flows spontaneously from hotter to colder regions of matter (or 'downhill' in terms of the temperature gradient).
The Clausius theorem (1855), also known as the Clausius inequality, states that for a thermodynamic system (e.g. heat engine or heat pump) exchanging heat with external thermal reservoirs and undergoing a thermodynamic cycle, the following inequality holds.
Clausius statement: it is impossible to construct a device that operates in a cycle and produces no effect other than the transfer of heat from a lower-temperature body to a higher-temperature body. Figure 6.3.2 illustrates the Clausius statement.
Contrast the second law of thermodynamics statements according to Kelvin and Clausius formulations; Interpret the second of thermodynamics via irreversibility
This is the "second form" or Clausius statement of the second law. It is important to note that when it is stated that energy will not spontaneously flow from a cold object to a hot object, that statement is referring to net transfer of energy.
Clausius' Statement. Unless there is some work done, thermal energy never flows from a body at a colder temperature to a body at a hotter temperature. Kelvin's Statement. The conversion of thermal energy to work is never perfectly efficient.
The Clausius statement of the Second Law involves cyclic processes and engines. It can be stated as: m. It is impossible to construct a device which, operating in a cycle, will produce no other effect than the transfer of heat from a cooler to a warmer body.