Imagine life in flatland, which exists in two dimensional rather than three dimensional space. (with some modification, this model applies to gas molecules adsorbed on a flat surface.) a two-dimensional ideal classical gas of particles is confined to an area a. the number of states with momentum in the momentum range p to p + dp is 2t. apdp f (p)dp = h2 (a) show that the partition fumction associated with translational motion of one molecule of gas is given by: 2tamkt z1 h2 1 without proof 2a | ехp(-аp") рфр - you may use the result: e [4 marks (b) explain why the partition function for translational motion of n molecules of the gas is given by 12tlamkt = z h2 n! [2 marks] (c) (i find an expression for the helmholtz free energy associated with translational motion for this gas. (ii) show that the entropy of the gas is given by 2tmkt a + in s=nkin [8 marks] (d) (i find the average translational energy of the gas and comment on whether this is the expected value (ii) find the chemical potential of the gas as a function of temperature.

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    m₁v₁ + m₂v₂ = (m₁ + m₂)vmomentum is conserved.the left-hand side of the equation represents the momentum in the system before the collision.the right-hand side represents the momentum in the system after the collisionm₁ and v₁ represents the mass and the velocity of the physics blockm₂ and v₂ represents the mass and velocity of the ball of puttyv represents the final velocity of the combined mass.the question states the two masses stick together. they combined mass has its own velocity with the body mass the sum of the two objects' massestheir combined momentum is (m₁ + m₂)vto find the magitude of (m₁ + m₂)v, we need to add the vectors on the left-hand side of the equation: m₁v₁ + m₂v₂.note the diagram. i have positioned the vectors in accordance with their directions.the magnitude of the resultant can be calculated using the pythagorean theorem since this is a right triangle situation (north and west are perpendicular)|(m₁ + m₂)v| =  √[ (m₁v₁)² + (m₂v₂)² ]|(m₁ + m₂)v| =  √[ (1.5kg·8.0m/s)² + (0.40kg·20m/s)² ]|(m₁ + m₂)v| =  14.4 kg m/sfor two significant figures (assuming that 20m/s is two), this rounds to 14 kg m/s

The correct answer should be b let me know if i’m wrong