Question

Two vessels A and B are filled with same gas where volume, temperature and pressure in vessel A is twice the volume, temperature and pressure in vessel B. Calculate the ratio of number of molecules of gas in vessel A to that in vessel B. 

Answer 1

Given : V_A = V_B , T_A=2T_B  P_A=2P_B

PV=Nk_BT

∴ No of molecules, N=PV/k_BT

N_A=P_AV_A/k_BT_A   and N_B=P_BV_B/k_BT_B

∴ N_A/N_B = (P_A/P_B)(V_A/V_B)(T_B/T_A) = (2)(2)(1/2)=2

2 is the required ratio.