Miscellaneous Modes of Thermodynamic Work P M V Subbarao Professor Mechanical Engineering Department I I T Delhi More forms of work driving the Industry & Nature!!!

Why cutting of a solid consumes power?

Why cutting occurs at A Particular value of stress?

Who controls the Growth Shape & Equilibrium Shape of A Crystal

Who decides the beauty of Table Cloth ???

The Role of Surface Tension in Engineering When splitting a solid, the amount of energy required is 2  A, where 2A is the area created (one A on each side). This energy is less than that needed just to break the bonds, since there is atomic and electronic relaxation. The surface energy is always positive because the atoms are less bound at the surface. The surface tension can be defined as the reversible work of formation of a unit area of surface at constant T, V, m. The surface tension is the two-dimensional analog to the pressure.

Surface Tension On the surface there are atoms on one side only, so there is a net inward cohesive force. This creates a force on the surface that tries to minimise its area. When considered as a force rather than an energy, the force is called "surface tension".

The tendency to minimize surface energy is a defining factor in the morphology and composition of surfaces and interfaces. This Is important for Solids & Liquids. The relative change in internal energy of a control mass w.r.t. change in surface area at constant temperature, volume. Law of a Nature: Thermodynamic Definition of Surface Tension

Materialg J/m 2 Tungsten (solid)2.9 Iron (solid)2.2 Iron (liquid)1.9 MgO1.2 Mercury (liquid)0.5 Water0.07 Acetic acid0.03 Nitrogen (liquid)0.01 Helium (liquid) Values of Surface Tension for Selected Materials

Work Associated with the Stretching of a Liquid Film

Blood Vessels & Blood Pressure For a cylinder of radius R and length l such as a blood vessel, the wall supplies an inward force and the liquid supplies an outward pressure. Infinitesimal work to be done by blood on vessel: This work is stopped by surface tension of the blood vessel material

There is a greater pressure difference for a smaller radius than a larger one. This inverse relationship is called Laplace's law.

The Faraday’s Work : An Amazing form of Work Transfer Consider a conducting rod PQ moving at a steady speed V perpendicular to a field with a flux densityB. An electron (negative charge e) in the rod will experience a force (= Bev) that will push it towards the end P.

Description of Work done by A Conductor The same is true for other electrons in the rod, so the end P will become negatively charged, leaving Q with a positive charge. As a result, an electric field E builds up until the force on electrons in the rod (unit length) due to this electric field (= Ee) balances the force due to the magnetic field Force per unit charge on Rod of unit length:

For a rod of length L, define the EMF as : What happens when the EMF drives a current in an external circuit? To do this, imagine that the rod moves along a pair of parallel conductors that are connected to an external circuit

Electrical Loading of Conductor The EMF will now cause a current to flow in the external resistor R. This means that a similar current flows through the rod itself giving a magnetic force, BIL to the left.

Quantification of the Faraday’s Work L is now the separation of the two conductors along which the rod PQ moves. An equal and opposite force (to the right) is needed to keep PQ moving at a steady speed. In a time dt, the rod moves a distance dx = Vdt Infinitesimal Work done on the rod

The Pairs of Work Transfers Energy dissipated in R = power x time = EMF  I× t Giving : B × I × L ×V × t = EMF × I × t or, as before, EMF = B × V × L 48.html

Generation of Shaft Work Energy transmission with a rotating shaft is very common in engineering practice. A force F acting through a moment arm r generates a torque T of

Isothermal Process of Real Gases in a Control Mass Van der Waals EOS

Displacement Work done by Superheated Steam During An Isothermal Process

Spring Work