Question

55. Two gases of equal masses are in thermal equilibrium. if Pa,Pb and Va, V b 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 = PbVb​

Answer 1

Hi There!

Explanation:

Two gases of equal mass means number of moles are constant while thermal equilibrium means temperature is constant.

In the ideal gas equation, PV = nRT, nRT is a complete constant because

• R is already a Gas Constant
• Temperature is constant
• Number of moles are constant

So PV = constant (this is also called Boyle's Law)

This means that now for any gas with respective voume and pressure, their product will remain same (constant).

Hence PaVa = PbVb is the required answer

Answer:

Option (D)

Answer 2

Question :-

$\sf \: two \: gases \: of \: equal \: masses \: are \: in \: thermal \\ \sf \: equilibrium. \: if \: p_{a} \: p_{b} \: and \: v_{a} \: v_{b} \: are \: their \: \\ \sf \: respective \: pressures \: and \: volumes \\ \sf \: then \: which \: relation \: is \: true \: -$

1. $\sf \: 2 p_{a} v_{a} = p_{b} v_{b}$
2. $\sf \: p_{a} + p_{b} ≠ \: v_{a} +v_{b}$
3. $\sf \: \frac{p_{a}}{v_{a}} = \frac{p_{b}}{p_{b}}$
4. $\sf \: p_{a}v_{a} = p_{b}v_{b}$

AnsweR :-

Given that, two gases of equal masses are in thermal equilibrium.

So, the the number of moles are constant and temperature is constant.

We know that :-

• $\sf \: for \: the \: ideal \: gas \: equation \implies \\ \\ \sf \: pv = nrt \:$

$\star \sf \: where \: n\: is \: the \: number \: of \: moles \: \\ \\ \star \sf \: r \: is \: universal \: gas \: constant \\ \\ \star \sf \: t \: is \: tempreature$

But in the Given Question :-

$\star \sf \: n \: (number \: of \: moles) \: are \: constant \\ \\ \star \sf \: t (tempreature) \: is \: costant \: \\ \\ \star \sf \: r \: (gas \: constant) \: is \: alread \: a \: constant$

So we can say that PV is constant.

We know that :-

According to Boyle's law , the product of the respective pressure and volumes of any gas will be equal.

So ,

$\large \implies \boxed{ \sf \: p_{a}v_{a} = p_{b}v_{b}}$

Hence, the option D is correct.

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Hope it will help you :)