First Law of a Closed System Undergoing a Cycle
First Law of a Closed System Undergoing a Cycle :
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Fig.1 First Law of Thermodynamics |
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Fig.1 First Law of Thermodynamics |
Symmetry difference of sets Let A and B be two sets. The symmetry difference of sets A and B is the set (A-B) ∪ (B-A) and it is denoted by A ∆ B. Then A∆B=(A-B) ∪ (B-A) = {x : x ∉ A ∩ B}. In Fig 9 shaded region represents A∆B Fig (9) Example…
Ordered pairs An ordered pairs consists of two objects or elements in a given fixed order. For example, if A and B are any two sets, then by an ordered pair of elements we mean a pair (a, b) in that order, where a ∈ A, b ∈…
Function as a set of ordered pairs Let A and B be two non-empty sets. A relation f from A to B i.e a subset of A × B is called a function (or a mapping or a map) from A to B, if i) for each a ∈ A there exists b ∈ B…
Theorem 3 The total number of subsets of a finite set containing n elements is 2ⁿ. Proof Let A be a finite set containing n elements.Let 0 ≤ r ≤ n. Consider those subset,of A that have r elements each.We know that the number of ways in which r elements can be chosen…
Open interval If a and b are two real numbers such that a < b, then the set of all real numbers x satisfying a x b is called an open interval and is denoted by (a, b) or ]a, b[ . Thus, (a,b) = (x: x ∈ R, a < x < b).
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