Final answer:
The correct expression for pressure equivalent to kinetic energy is c) P = mv²/2, which is derived from the relationship of pressure to kinetic energy per unit volume in the kinetic theory of gases and Bernoulli's equation.
Step-by-step explanation:
The question is essentially asking to find the expression for pressure that corresponds to the kinetic energy of an object. The correct relation for kinetic energy (K.E.) is K.E. = ½mv², where m is mass and v is velocity. According to the kinetic theory of gases, pressure (P) can be related to the kinetic energy of the particles in a gas and is given by the equation PV = ⅓m², where P is the pressure, V is the volume, m is the mass of a molecule, and v² is the average of the molecular speed squared.
Therefore, the equivalent pressure due to kinetic energy is c) P = mv²/2 which is the kinetic energy per unit volume. In Bernoulli's equation, this relationship of pressure and kinetic energy is evident as every term has units of energy per volume, and when we consider kinetic energy in terms of pressure, it's represented by the term p²/2 in the equation PV = Nmv², which reiterates the form of the kinetic energy equation. Also, this is consistent with the thermal energy of gases, which is proportional to the average translational kinetic energy of atoms and molecules, defined as KE = ½m² = 3kT.