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?

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A

$2p_a V_a = p_b V_b$

10%

B

$p_a ≠ p_b, V_a = V_b$

6%

C

$\frac{p_a}{V_a} = \frac{p_a}{V_b}$

22%

D

$p_a V_a = p_b V_b$

62%

Solution:

When the gases are in thermal equilibrium, it means the temperature of the gases are same, therefore according to Boyle's law
$ \, \, \, \, \, \, \, p_1 V_1 = p_2 V_2$
$Here \, \, \, \, \, \, \, \, \, \, p_1 = p_a$
$ \, \, \, \, \, \, \, \, \, \, \, \, \, V_1 = V_a$
$\, \, \, \, \, \, \, \, \, \, \, \, \, \, p_2 = p_b$
$ \, \, \, \, \, \, \, \, \, \, \, \, \, V_2 = V_b$
$ Hence, \, \, \, \, \, \, \, \, \, \, p_a V_a = p_b V_b$

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