A container has two chambers of volumes V_1=2 litres and V_2=3 litres separated by a partition made of a thermal insulator. The chambers contains n_1=5 and n_2=4 moles of ideal gas at pressures p_1=1 ~atm and p_2=2 ~atm , respectively. When the partition is removed, the mixture attains an equilibrium pressure of :
B. 1.6 atm
By energy conservation aligned & E _1+ E _2= E _ mix \\ & n _1 f _1 RT _1 2 + n _2 f _2 RT _2 2 = ( n _1 n _2 ) fRT _ mix 2 \\ & 3 2 P _1 ~V _1+ 3 2 P _2 ~V _2= 3 2 P _ mix ( V _1+ V _2 ) \\ & 3 2 1 2+ 3 2 2 3= 3 2 P _ mix (5) \\ & P _ mix = 8 5 \\ & P _ mix =1.6 ~atm aligned
Related: Physics — Thermodynamics · All PYQ Banks