In mathematics, a critical point of a function is where its derivative is zero or undefined, indicating potential local maxima, minima, or saddle points. In thermodynamics, a critical point refers to the end point of a phase equilibrium curve, beyond which distinct liquid and gas phases do not exist, marking the critical temperature and pressure of a substance.

Critical Point

critical point of a function

derivative is zero

Local maxima are points in a function where the function value is higher than all nearby points, representing a peak in the function's graph. They are crucial in optimization problems, helping to identify optimal solutions within a specific region of the domain, but may not represent the absolute highest point of the entire function, known as the global maximum.

local maxima

Local minima are points in a function where the function value is lower than at any nearby points, making them crucial in optimization problems. They can pose challenges in finding the global minimum, especially in complex, multi-dimensional spaces where algorithms might get 'stuck' at these points instead of finding the true lowest point.

Local Minima

saddle points

Critical point in thermodynamics

phase equilibrium curve

distinct liquid and gas phases

Critical temperature is the highest temperature at which a substance can exist as a liquid, regardless of pressure, marking the end of the liquid-gas phase boundary. Above this temperature, the substance becomes a supercritical fluid, exhibiting unique properties that are distinct from typical liquid or gas states.

critical temperature

Critical pressure is the minimum pressure required to liquefy a gas at its critical temperature, beyond which the substance cannot exist as a liquid regardless of the pressure applied. It is a fundamental property in thermodynamics that helps determine the behavior of substances in various states of matter and is crucial for understanding phase transitions and the design of industrial processes.

Relevant Degrees

Your Lessons