Two gases of equal masses are in thermal equilibrium. If Pa,Pb and Va,Vb are their respective pressures and volumes, then which relation is true?

Question

Two gases of equal masses are in thermal equilibrium. If Pa,Pb and Va,Vb are their respective pressures and volumes, then which relation is true? (A)  2PaVa=PbVb  (B)  Pa≠ Pb,Va=Vb  (C)  (Pa/Va)=(Pb/Vb)  (D)  PaVa=PbPv

Tardigrade Admin · Accepted Answer

When the gases are in thermal equilibrium, it means the temperature of the gases are same, therefore according to Boyles law P1V1=P2V2 Here: P1=Pa V1=Va P2=Pb V2=Vb Hence, PaVa=PbVb

Q. Two gases of equal masses are in thermal equilibrium. If $P_{a}, P_{b}$ and $V_{a}, V_{b}$ are their respective pressures and volumes, then which relation is true?

$2 P_{a} V_{a} = P_{b} V_{b}$

$P_{a} \neq = P_{b}, V_{a} = V_{b}$

$\frac{P _{a}}{V _{a}} = \frac{P _{b}}{V _{b}}$

$P_{a} V_{a} = P_{b} P_{v}$

When the gases are in thermal equilibrium, it means the temperature of the gases are same, therefore according to Boyles law $P_{1} V_{1} = P_{2} V_{2}$ Here: $P_{1} = P_{a}$ $V_{1} = V_{a}$ $P_{2} = P b$ $V_{2} = Vb$ Hence, $P_{a} V_{a} = P_{b} V_{b}$

Q. Two gases of equal masses are in thermal equilibrium. If Pa​,Pb​ and Va​,Vb​ are their respective pressures and volumes, then which relation is true?

2Pa​Va​=Pb​Vb​

Pa​=Pb​,Va​=Vb​

Va​Pa​​=Vb​Pb​​

Pa​Va​=Pb​Pv​