Author: Saim Khalid

Forming an intermediate state between liquids, in which we assume no external pressure, and gases, in which we omit molecular forces, we have the state in which both terms occur. As a matter of fact, we shall see further on, that this is the only state which occurs in nature. van der Waals (1873, ch2)…

There cannot be a greater mistake than that of looking superciliously upon practical applications of science. The life and soul of science is its practical application. In the first four chapters, we have concentrated on applications of the first and second laws to simple systems (e.g., turbine, throttle). The constraints imposed by the second law…

S = k ln W L. Boltzmann We have discussed energy balances and the fact that friction and velocity gradients cause the loss of useful work. It would be desirable to determine maximum work output (or minimum work input) for a given process. Our concern for accomplishing useful work inevitably leads to a search for…

A theory is the more impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended is its area of applicability. Therefore the deep impression which classical thermodynamics made upon me. Albert Einstein Having established the principle of the energy balance for individual systems, it…

When you can measure what you are speaking about, and express it in numbers, you know something about it. When you cannot measure it, your knowledge is meager and unsatisfactory. The energy balance is based on the postulate of conservation of energy in the universe. This postulate is known as the first law of thermodynamics. It…

“Aside from the logical and mathematical sciences, there are three great branches of natural science which stand apart by reason of the variety of far reaching deductions drawn from a small number of primary postulates. They are mechanics, electromagnetics, and thermodynamics. These sciences are monuments to the power of the human mind; and their intensive…

Problem: Find the integral: ∫(4×3) dx\int (4x^3) \, dx∫(4×3)dx Solution: ∫4×3 dx=x4+C\int 4x^3 \, dx = x^4 + C∫4x3dx=x4+C Answer = x4+Cx^4 + Cx4+C

Problem: The marks of 5 students are: 60, 70, 80, 90, 100. Find the mean. Solution: Mean=Sum of marksNumber of students\text{Mean} = \frac{\text{Sum of marks}}{\text{Number of students}}Mean=Number of studentsSum of marks​ =60+70+80+90+1005=4005=80= \frac{60+70+80+90+100}{5} = \frac{400}{5} = 80=560+70+80+90+100​=5400​=80 Mean = 80

Problem: A right triangle has an angle of 30∘30^\circ30∘ and the hypotenuse is 10. Find the opposite side. Solution: sin⁡(30∘)=oppositehypotenuse\sin(30^\circ) = \frac{\text{opposite}}{\text{hypotenuse}}sin(30∘)=hypotenuseopposite​ 12=opposite10\frac{1}{2} = \frac{\text{opposite}}{10}21​=10opposite​ opposite=5\text{opposite} = 5opposite=5 Opposite side = 5

Problem:Find the derivative of: f(x)=x2+3xf(x) = x^2 + 3xf(x)=x2+3x Solution: f′(x)=2x+3f'(x) = 2x + 3f′(x)=2x+3 Derivative = 2x+32x + 32x+3