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- In which situation's would angular acceleration be negative? Select all that apply 1. An object is at rest and is starting to rotate clockwise 2. An object is rotating clockwise and speeding up 3. An object is rotating clockwise and speeding up 4. An object is rotating counterclockwise and slowing downThe potential function between molecules of a simple non-polar gas, when the mass centres are separated by a distance r, is given by the well-known expressions: p(r) = 4€[(÷) '? – (#)*] For this gas in question: e/k = 120K and b, = No =0.063 m³/kmol a) What is the magnitude of the potential o(r) at its minimum?Q.2 A gas in which the pressure and the density are connected by the adiabatic relation p= kp' flows along a pipe. Prove that 3Y P- constant y-1 p if the external forces are neglected, v being the speed. If the pipe converges in the direction of the flow, prove that v will increase and p/p will diminish in the direction of flow provided that v'p < Yp.
- For the machine element shown, locate the y coordinate of the center of gravity.Find an expression for (∂H/∂P) T for a gas obeying the van der Waals equation of state.Suppose that a 1.00 cm' box in the shape of a cube is perfectly evacuated, except for a single particle of mass 1.00 × 10 g. The particle is initially moving perpendic- ular to one of the walls of the box at a speed of 400 m/s. Assume that the collisions of the particle with the walls are elastic. (a) Find the mass density inside the box. (b) Find the average pressure on the walls perpendi- cular to the particle's path. (c) Find the average pressure on the other walls. (d) Find the temperature inside the box. Discuss the as- sumption of elastic collisions, in light of this result.
- For a dilute gas of N monatomic particles with mass m and total energy E, use the Sackur- Tetrode equation for the entropy S V = log + NkB to derive expressions for the pressure and internal energy in terms of the temperature T and volume V. [You may use that X₁ = 3πh² N/(mE).] th4) A surface with No adsorption centers has N (S N,) gas molecules adsorbed on it. Show that the chemical potential of the adsorbed molecules is given by u = kTIn- N (No-N)a(T) where a(T) is the partition function of a single adsorbed molecule. Solve the problem by constructing the grand partition function as well as the partition function of the system. [Neglect the intermolecular interaction among the adsorbed molecules.]Calculate the Helmholtz free energy (∆A) of an ideal gas when 2.0 mol expands isothermally from 1.5 to 3.5 cm3 at 120°C