Assuming (for simplicity) that CV and Cp are independent of temperature, these differentials can be integrated directly from state 1 to state 2:
These equations apply to both reversible and irreversible changes because they contain only state functions.
Isentropic changes in ideal gases depend on the ratio of the specific heats:
This ratio is 1.67 for monatomic gases and 1.4 for diatomic gases. Since the difference in specific heats of an ideal gas is Cp - Cv = R, the following formulas express the specific heats in terms of their ratio and their difference:
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Do we really want the one thing that gives us its resources unconditionally to suffer even more than it is suffering now? Nature, is a part of our being from the earliest human days. We respect Nature and it gives us its bounty, but in the recent past greedy money hungry corporations have made us all so destructive, so wasteful.