A cylindrical container is initially separated by a clamped

A cylindrical container is initially separated by a clamped piston into two compartments of equal volume. The left compartment is filled with one mole of neon gas at a pressure of 4 atm and the right with an unknown number of moles of argon gas at 1 atm. The gases may be considered as ideal. The whole system is initially at temperature T = 300 K, and is thermally insulated from the outside world. The piston is then unclamped and released to move freely without friction. Eventually it comes to rest in an equilibrium position. (i) What is the initial ratio of the pressures of argon to neon in terms of n (the number of moles of each gas) (ii) What is the new temperature of the system? (iii) After the piston comes to rest what is the ratio of the final pressure of argon to the final pressure of neon? (iv) Write an expression for the final volume of argon in terms of initial volume, and initial and final argon pressures. (v) What is the ratio of the final volume of argon to neon? (vi) What is the ratio between the initial to final volume of argon? (vii) What is the ratio between the initial to final volume of neon?

Solution

(i)    initial ratio of the pressures of argon to neon =   n : 1    = n / 1 = 1   : 4

         where, n   = 0.25 moles of argon gas

(ii)    the new temperature of the system = 300 K

(iii)    the ratio of the final pressure of argon to the final pressure of neon = 1 : 1

(iv)   final volume of argon in terms of initial volume =       V_final = 0.4 V_initial

      As   , Vfinal = 2.463     and    Vinitial = 6.1575

          Initial Pressure   = 1 atm          Final pressure   = 2.5 atm

          =>   P_final = 2.5 P_initial

(v)   ratio of the final volume of argon to neon = 1 : 4

(vi)    ratio between the initial to final volume of argon   =   2.5 : 1

(vii)    the ratio between the initial to final volume of neon = 0.625 : 1