Skip to main content

HEAT AND THERMODYNAMICS

By
U

                       HEAT AND THERMODYNAMICS

       Thermodynamics deals with various phenomena of energy and related properties of matter, especially the transformation of heat into other forms of energy. An example of such transformation is the process converting heat into mechanical work. Thermodynamics thus plays central role in technology, since almost all the raw energy available for our use is liberated in the form of heat. in this topic we shall their significance and applications.

              KINETIC THEORY OF GASES 

     The behavior of gases is well accounted for by the kinetic theory based on microscopic approach. Evidence in favor of the theory is exhibited in diffusion of gases and Brownian motion of smoke particles etc.

     The following postulates help to formulate a mathematical model of gases.
  1.      A finite volume of gas consists of very large number of molecules.
  2.      The size of the molecules is much smaller then the separation between molecules.
  3.      The gas molecules are in random motion and may change their direction of motion after every collision. 
  4.      Collision between gas molecules themselves and with walls of container are assumed to be perfectly elastic.
  5.      Molecules do not exert force on each other except during a collision. 

Comments

Post a Comment

Popular posts from this blog

PROBABILITY

By
                                        PROBABILITY                          INTRODUCTION                                                                   The word probability has two meaning:(1) a quantitative measure of uncertainty and (2) a measure of degree of belief in a particular or problem.                                Probability and statistic are fundamentally interrelated. probability is often called the vehicle of statistics. the area of inferential statistics in which we are mainly concerned with drawing inferences from experiments or situations ...
Post a Comment
Read more

SETS

By
                                             SETS       INTRODUCTION           We often speak some words in daily life which represent a collection of things, for example, a team of players, a bunch of flowers, a cluster of trees, a group of friends, a swarm of birds and so on. But in mathematics, we can use a single word "set" to denote all such type of words that show the collection of things such as, a set of players, a set of flowers, a set of trees, a set of friends and a set of birds, etc. Thus we can define a set as:     "A collection of distinct and well-defined objects is called a set. "  The objects of a set are called its members or elements.    ...
Post a Comment
Read more

Banach Contraction Principle

By
Banach Contraction Principle Let (X,d) be a complete metric space, then each contraction map f : X → X has a unique fixed point. Let h be a contraction constant of the mapping f . We will explicitly construct a sequence converging to the fixed point. Let x0 be an arbitrary but fixed element in X. Define a sequence of iterates {xn} in X by xn = f(xn−1) (= f n(x0)), for all n ≥ 1. Since f is a contraction, we have d(xn, xn+1) = d(f(xn−1), f(xn)) ≤ hd(xn−1, xn), for any n ≥ 1. Thus, we obtain d(xn, xn+1) ≤ hnd(x0, x1), for all n ≥ 1. Hence, for any m > n, we have d(xn, xm) ≤  hn +hn+1 +···+hm−1 d(x0, x1) ≤ hn 1−h d(x0, x1). We deduce that {xn} is Cauchy sequence in a complete space X. Let xn → p ∈ X. Now using the  continuity of the map f , we get p = lim n→∞ xn = lim n→∞ f(xn−1) = f(p). Finally, to show f has at most one fixed point in X, let p and q be fixed points of f . Then, d(p,q) = d(f(p), f(q)) ≤ hd(p,q). Since h < 1, we must have p = q The proof of the BCP yields the ...
Post a Comment
Read more