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Standard X

Physics

Ideal Gas Equation

A gas has the...

Question

A gas has the thermodynamic variables $P, V$ and $T$ and is in container $A$ . Another gas in container $B$ has variables $2 P, V / 4$ and $2 T$ . Find the ratio of molecules in container $A$ and $B$ .

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Solution

$P V = n R T$
$∴ \frac{P V}{T} = n R$
$∴ \frac{P_{A} V_{A}}{T_{A}} = n_{A} R$
And , $\frac{P_{A} V_{A}}{T_{A}} =$ $\frac{P V}{T}$
and, $\frac{P_{B} V_{B}}{T_{B}} =$ $\frac{2 P V}{2 T \times 4}$ $= \frac{P V}{4 T}$
$∴ \frac{n_{A}}{n_{B}} = (\frac{P_{A} V_{A}}{T_{A}}) /$ $(\frac{P_{B} V_{B}}{T_{B}}) = 4$

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A gas has the thermodynamic variables P,V and T and is in container A. Another gas in container B has variables 2P,V/4 and 2T. Find the ratio of molecules in container A and B.

PV=nRT∴PVT=nR∴PAVATA=nARAnd , PAVATA=PVTand, PBVBTB=2PV2T×4=PV4T∴nAnB=(PAVATA)/(PBVBTB)=4

A gas has the thermodynamic variables $P, V$ and $T$ and is in container $A$ . Another gas in container $B$ has variables $2 P, V / 4$ and $2 T$ . Find the ratio of molecules in container $A$ and $B$ .