P = (2/3)*n*E,
n = N/V,
p0 = (2/3)*(N1/V1)*E1;
4p0 = (2/3)*(N2/V2)*E2;
3p0 = (2/3)*( (N1+N2)/(V1+V2) )*E3;
N1*E1 + N2*E2 = (N1+N2)*E3;
N1*E1 = 3*p0*(V1)/2;
N2*E2 = 3*4p0*(V2)/2;
(N1+N2)*E3 = 3*3p0*(V1+V2)/2;
( 3*p0*(V1)/2 ) + ( 3*4p0*(V2)/2 ) = 3*(3p0)*(V1+V2)/2;
теперь сокращая всё ненужное в последнем уравнении получим:
V1 + 4V2 = 3*(V1 + V2);
V1 + 4V2 = 3V1 + 3V2;
V2 = 2V1;
V2/V1 = 2/1.