Solution:
From the ideal gas law, \(PV = N k_B T\) which gives \(N = \frac{PV}{k_B T}\). Taking the ratio: \(\frac{N_B}{N_A} = \frac{P_B V_B / T_B}{P_A V_A / T_A} = \frac{2P times (V/2) / 2T}{PV / T} = \frac{1}{2}\).
A vessel contains gas A at pressure \(P\), volume \(V\) and temperature \(T\). Another vessel contains gas B at pressure \(2P\), volume \(\frac{V}{2}\) and temperature \(2T\). Ratio of number of molecules of B to A will be
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