<P> The concept of entropy arose from Rudolf Clausius's study of the Carnot cycle . In a Carnot cycle, heat Q is absorbed isothermally at temperature T from a' hot' reservoir and given up isothermally as heat Q to a' cold' reservoir at T . According to Carnot's principle, work can only be produced by the system when there is a temperature difference, and the work should be some function of the difference in temperature and the heat absorbed (Q). Carnot did not distinguish between Q and Q, since he was using the incorrect hypothesis that caloric theory was valid, and hence heat was conserved (the incorrect assumption that Q and Q were equal) when, in fact, Q is greater than Q . Through the efforts of Clausius and Kelvin, it is now known that the maximum work that a heat engine can produce is the product of the Carnot efficiency and the heat absorbed from the hot reservoir: </P> <Dl> <Dd> <Table> <Tr> <Td> <P> W = (T H − T C T H) Q H = (1 − T C T H) Q H (\ displaystyle W = \ left ((\ frac (T_ (H) - T_ (C)) (T_ (H))) \ right) Q_ (H) = \ left (1 - (\ frac (T_ (C)) (T_ (H))) \ right) Q_ (H)) </P> </Td> <Td> <Table> <Tr> <Td> <P> </P> </Td> <Td> <P> </P> </Td> <Td> <P> </P> </Td> </Tr> <Tr> <Td> <P> </P> </Td> </Tr> </Table> </Td> <Td> <P> (1) </P> </Td> </Tr> </Table> </Dd> </Dl> <Dd> <Table> <Tr> <Td> <P> W = (T H − T C T H) Q H = (1 − T C T H) Q H (\ displaystyle W = \ left ((\ frac (T_ (H) - T_ (C)) (T_ (H))) \ right) Q_ (H) = \ left (1 - (\ frac (T_ (C)) (T_ (H))) \ right) Q_ (H)) </P> </Td> <Td> <Table> <Tr> <Td> <P> </P> </Td> <Td> <P> </P> </Td> <Td> <P> </P> </Td> </Tr> <Tr> <Td> <P> </P> </Td> </Tr> </Table> </Td> <Td> <P> (1) </P> </Td> </Tr> </Table> </Dd> <Table> <Tr> <Td> <P> W = (T H − T C T H) Q H = (1 − T C T H) Q H (\ displaystyle W = \ left ((\ frac (T_ (H) - T_ (C)) (T_ (H))) \ right) Q_ (H) = \ left (1 - (\ frac (T_ (C)) (T_ (H))) \ right) Q_ (H)) </P> </Td> <Td> <Table> <Tr> <Td> <P> </P> </Td> <Td> <P> </P> </Td> <Td> <P> </P> </Td> </Tr> <Tr> <Td> <P> </P> </Td> </Tr> </Table> </Td> <Td> <P> (1) </P> </Td> </Tr> </Table>

The term entropy refers to the measure of what aspect of a system