| Entropy |
| Another state function of fundamental importance is entropy. While both heat and work are forms of energy, it was found that all of heat could not be converted into useful work. Some heat always gets degraded as heat absorbed and lost through the walls of pistons or lost in its flow from hot regions to cold regions without producing anything useful. |
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Carnot, in the 18 th century showed that even in a fully reversible cyclic process consisting of isothermal and adiabatic (a process wherein q = 0) expansions and compressions, heat cannot be fully converted into work and that the ratio work done by the system (not on the system) to the heat absorbed by the system is always less than 1. All these observations can be summarized through the Clausius inequality. |
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| dS  dq/T and dS = dq rev /T
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(21.13) |
This defines a new state function S, which is the ratio of the reversible heat divided by temperature. Combining eq (21.13) with the first law in a differential form |
| dU = dq + dw |
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| = TdS - PdV |
(21.14) |
| The subscript rev is not used in 21.14 because whether the process is reversible or not, the difference TdS-PdV is always equal to dU. |
