MHT CET · Physics · Thermodynamics
Two vessels separately contain two ideal gases \(A\) and \(B\) at the same temperature, pressure of A being twice that of B. Under such conditions, the density of A is found to be 1.5 times the density of \(B\). The ratio of molecular weights of \(A\) and \(B\) is
- A \(1: 2\)
- B \(2: 3\)
- C \(3: 4\)
- D \(2: 1\)
Answer & Solution
Correct Answer
(C) \(3: 4\)
Step-by-step Solution
Detailed explanation
For an ideal gas, \(\mathrm{PV}=\mathrm{RT}\) and \(\mathrm{M}=\rho \mathrm{V}\)
\(\begin{array}{ll}\therefore & \frac{P M}{\rho}=R T \\ \therefore & \frac{P_A M_A}{\rho_A}=\frac{P_B M_B}{\rho_B}\end{array}\)
\(\frac{M_A}{M_B}=\frac{\rho_A}{\rho_B} \times \frac{P_B}{P_A}=\frac{3}{2} \times \frac{1}{2}=\frac{3}{4}\)
\(\begin{array}{ll}\therefore & \frac{P M}{\rho}=R T \\ \therefore & \frac{P_A M_A}{\rho_A}=\frac{P_B M_B}{\rho_B}\end{array}\)
\(\frac{M_A}{M_B}=\frac{\rho_A}{\rho_B} \times \frac{P_B}{P_A}=\frac{3}{2} \times \frac{1}{2}=\frac{3}{4}\)
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