Osm Physics by Ashish

  The first law of thermodynamics is a statement of the law of conservation of energy applied to thermodynamic systems. When a small amount of heat d Q dQ is supplied to a thermodynamic system, a part of it may be used to increase the internal energy of the system, while the remaining part may be used to do external work . Thus, d Q = d U + d W \boxed{dQ=dU+dW} where d Q dQ = infinitesimal amount of heat supplied to the system, d U dU = infinitesimal change in internal energy, d W dW = infinitesimal work done by the system. If the system performs work d W dW against an external pressure P e x t P_{\rm ext} , d W = P e x t   d V \boxed{dW=P_{\rm ext}\,dV} Therefore, d Q = d U + P e x t   d V \boxed{dQ=dU+P_{\rm ext}\,dV} For a quasi-static process , P e x t = P P_{\rm ext}=P , so d Q = d U + P   d V \boxed{dQ=dU+P\,dV} ​

Motion Relative to Earth (Rotating Frame) Earth is a non-inertial (rotating) frame , so we add fictitious forces to apply Newton's laws. 1. Centrifugal Force (affects g ) Cause: Earth's rotation (every object, moving or not). Direction: Radially outward from the axis. Effect on g: g ′ = g − ω 2 R cos ⁡ 2 λ g ′ = g − ω 2 R cos 2 λ 2. Coriolis Force (affects moving objects) Cause: Motion relative to rotating Earth. Formula:   F ⃗ c o r = − 2 m ( ω ⃗ × v ⃗ ) F cor ​ = − 2 m ( ω × v ) Direction: Perpendicular to motion; does no work (changes direction only). Deflection: Right in N. Hemisphere, Left in S. Hemisphere. Examples: Cyclones, ocean currents, trade winds, Foucault pendulum, projectile drift.