A box containing N molecules of an ideal gas at temperature T₁ and pressure P₁. The number of molecules in the box is doubled keeping the total kinetic energy of the gas same as before. IF the new pressure is P₂ and temperature is T₂, then : 

P₂ = P₁, T₂ = T₁ / 2

Kinetic energy of N molecules of gas : \(E = \frac{3}{2} NkT\)

Initially, \(E_1 = \frac{3}{2}N_1kT_1\) and finally \(E_2 = \frac{3}{2}N_2kT_2\)

But according to \(E_1 = E_2\) and \(N_2 = 2N_1\)

\(\Rightarrow \frac{3}{2}N_1 k T_1 = \frac{3}{2} (2N_1)k T_2\)

\(\Rightarrow T_2 = \frac{T_1}{2}\)

Since, the kinetic energy is constant : 

\(\frac{3}{2} N_1 k T_1 = \frac{3}{2} N_2 k T_2\)

\(\Rightarrow N_1T_1 = N_2T_2\) Thus, NT = constant

From ideal gas equation of N molecule, PV = NkT

\(\Rightarrow P_1V_1 = P_2V_2\) Thus, P₁ = P₂ ... [As V₁ = V₂ and NT = constant]