A 3-dimensional ideal gas obeys pV = 3/2E, where p is the pressure, V is the volume, and E is the internal energy

Please see the attached file for full problem description. 1. We saw in class that a 3-dimensional ideal gas obeys pV = 3/2E, where p is the pressure, V is the volume, and E is the internal energy (average kinetic energy). Derive the corresponding formula for a two-dimensional ideal gas, i.e. a collection of noninteracting particles that moves on a plane. (Hint: suppose a two-dimensional ideal gas of N particles, with internal energy E, is confined by one-dimensional "walls" to an area A; the pressure is defined as the force per unit length). 2. Each r seconds a particle, which was initially x = 0, jumps either left or right (each with probability 1/2) a distance a. At time tn= nr, the p... click for more

Heat capacity of a gas in an x^n potential

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Internal energy of N particles in the potential V(x) = 1/2 m omega^2 x^2 + a x^4

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Macrostates, microstates and temperature of a system.

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Susceptibility of paramagnetic atoms

Could you please do the question attached? Thank you.