toEniConsider a system that consists of N noninteracting particles in a cubical container of edgelength L. Assuming that the force exerted by the ith particle in a collision with a wallδεperpendicularthex-direction is given bywhere2π²ħ² n² ny niyIZ+ +2mL LL₂m² = 3 (n²x + n², + n/² )₂2), prove that F22ix2Miyizixixprove that pressure P =2Ni = 1,2,..., N3VE=28,n;3LFix = -(a)n₁aLxIf _L₂ = L₁ = L₂ = Land(b) If the average force is defined as F = N(F₁x),). (c) From the result of (b), derive that the system obeys theideal gas law PV = Nk„T (hint: you can apply the equipartition of energy theorem for (s)).ni

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Consider a system that consists of N noninteracting particles in a cubical container of edge length L. Assuming that the force exerted by the ith particle in a collision with a wall where Fix the x-direction is given by perpendicular Eni to = 28m ▸ 3L n² = (²+²+²), prove that F = (b) If the average force is defined as F = N(F), 2 7²ħ² n²x My N²₂ + + 2mL LL 2 2N i=1,2,..., N (a) δε, ni ƏL If 9 L₁ = L₁ = L₁ = L and prove that pressure P = - E. 3V ). (c) From the result of (b), derive that the system obeys the deal gas law PV = Nk T (hint: you can apply the equipartition of energy theorem for (&)).

Consider a system that consists of N noninteracting particles in a cubical container of edge length L. Assuming that the force exerted by the ith particle in a collision with a wall where Fix the x-direction is given by perpendicular Eni to = 28m ▸ 3L n² = (²+²+²), prove that F = (b) If the average force is defined as F = N(F), 2 7²ħ² n²x My N²₂ + + 2mL LL 2 2N i=1,2,..., N (a) δε, ni ƏL If 9 L₁ = L₁ = L₁ = L and prove that pressure P = - E. 3V ). (c) From the result of (b), derive that the system obeys the deal gas law PV = Nk T (hint: you can apply the equipartition of energy theorem for (&)).