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Articles by Dr Pankaj Dumka
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Solving the First Law of Thermodynamics using Python
The first law of thermodynamics is related to energy conservation − if energy in one form disappears then the energy will appear in some other form. In thermodynamics we are primarily concerned about heat, work and internal energy. Heat and work are forms of energy called "energy in transit", making them path functions that cannot be stored by a system, whereas internal energy is a property of the system that can be stored. For a closed system, the first law is written as − $$\mathrm{\Sigma Q=\Sigma W}$$ This is only valid for a closed system undergoing a ...
Read MoreModelling the Rankine Cycle in Python
The Rankine cycle is the heart of any thermal power plant. A basic Rankine cycle has four processes: reversible adiabatic work interactions in turbine and pump, and isobaric heat interactions in boiler and condenser. A schematic of a thermal power plant is shown in the figure given below ? Boiler Turbine Condenser Pump ...
Read MoreModelling the Secant Method in Python
The Secant method is a powerful numerical technique for finding roots (x-intercepts) of polynomial or transcendental functions. Unlike the Newton-Raphson method, it doesn't require derivatives, making it more practical for complex functions. How the Secant Method Works The method starts by selecting two initial points (x₁, x₂) near the expected root. A secant line connects the corresponding points on the function curve. Where this line intersects the x-axis gives us the next approximation x₃ ? ...
Read MoreModelling the Regula Falsi Method in Python
The Regula Falsi Method, also known as the "False Position Method", is a numerical technique for finding roots of equations. It uses linear interpolation between two points that bracket the root to iteratively converge to the solution. ...
Read MoreModelling the Newton Raphson Method in Python
In this tutorial, we will explore how to find roots of polynomial or transcendental equations using the Newton-Raphson method. This is an iterative numerical method that starts with an initial guess and converges to the root through successive approximations. x_g, f(x_g) x_n Newton-Raphson Method x f(x) ...
Read MoreModelling the Projectile Motion using Python
Projectile motion is the motion of an object thrown into the air under the influence of gravity. Python provides excellent tools for modeling and visualizing this physics concept using mathematical equations and plotting libraries. ...
Read MoreModelling the Carnot Cycle in Python
The Carnot cycle is the most fundamental gas power cycle that serves as a benchmark for all engine cycles. Every engine cycle efficiency is validated against the Carnot cycle's theoretical maximum efficiency. It comprises four processes: two reversible adiabatic processes and two isothermal processes. ...
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