One cubic meter (1 m³) of mono-atomic ideal gas, is initially at room temperature and atmo-spheric pressure. The mass of a single molecule is 1.34 × 10-26kg.1. Find the root mean square speed, vrms, Oof the molecules by equating the kinetic energyof a single molecule to its average thermal energy.2. Knowing that the gas obeys the Maxwell speed distribution3/24nv²e-2Tmmu2D(v) =(0.2)2πkTsuch thatD(v)dv = 1.(0.3)Find the expression of the probability (do not do the integral) that a particular moleculeis moving with a speed faster than 2000m/s.3. The gas is heated at constant pressure until it triples in volume. Calculate the increasein its entropy. 5. As we showed in the class, the total partition function of N molecules readsZNhN N!(0.5)%DUse Z, and Equation (0.4) to find the pressure of the relativistic gas, P, as a function ofV, N, T.6. Find the total thermal energy of the relativistic gas U. Show that the relation betweenthe pressure, total thermal energy and Volume for a relativistic gas is given by

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