Clausius Inequality is not only for reversible process
Since overall (system + surrounding) entropy always increase.
(∆s) system + surrounding ≥ 0
For a cyclic process (∆s) system = 0
So (∆s) surrounding ≥ 0
Note that in cyclic integral of (dQ/T) dQ is positive for heat entering system form surrounding.
So for surrounding change in entropy after a cyclic process is given by
cyclic integral of (-dQ/T) which is ≥ 0
Thus cyclic integral of (dQ/T) ≤ 0
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Uncirculated coins go through the normal minting process, but are then removed and placed into sets for collectors. Proof coins are made on specialized dies to achieve better detail and more shine in the finish.
contradiction
A geometry proof is a step-by-step explanation of the process you took to solve a problem. Instead of using numbers, you use words. There are two types of proofs: a paragraph proof, and a column proof. The column proof is the most common proof. In this proof, you must set up a t-chart. On the left side, you must write the steps you took to solve the problem. Make sure you number each step. On the right side, explain why you took this step. Make sure to number each explanation with the same number as the step on the left side you are explaining. Sources: Calculus III Student in 12th grade Took geometry in 8th grade
No. Proof is a type of coin, not a grade. Most coins made are meant for circulation, but some are proof varieties, which are made with a slightly different process to make them much more shiny and are sold to collectors. The highest grade using the Sheldon Scale is MS-70. MS stands for mint state, and it's on a scale from 1 to 70.
I am not really sure what you are asking but there are 3 types of proofs in geometry a flow proof, a 2-collumn proof, and a paragraph proof.