A vessel has $x$ $g$ of gas at high pressure $P$ . When certain gas escapes, the pressure $P$ became $P / 8$ and temperature $T$ became $2 T$ . What is the amount of gas escaped?

\frac{2}{3} m

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\frac{1}{3} m

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\frac{15}{16} m

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\frac{3}{4} m

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Solution

The correct option is C $\frac{15}{16} m$
x g of gas= $\frac{x}{M}$ mole of gas (n).
As the volume is constant $P \propto n T$
Pressure= $P_{1}$ =P and $P_{2} = \frac{P}{8}$
Temperature= $T_{1}$ =T and $T_{2} = 2 T$
Now, $\frac{P_{1}}{T_{1} n_{1}} = \frac{P_{2}}{T_{2} n_{2}} ⟹ \frac{P}{\frac{x}{M} \times T} = \frac{\frac{P}{8}}{n_{2} \times 2 T} ⟹ n_{2} = \frac{\frac{x}{M}}{16}$
$∴ (1 - \frac{1}{16}) x g = \frac{15 x}{16} g$ of the gas escaped.

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A vessel has x g of gas at high pressure P. When certain gas escapes, the pressure P became P/8 and temperature T became 2T. What is the amount of gas escaped?

The correct option is C 1516mx g of gas=xM mole of gas (n).As the volume is constant P∝nTPressure=P1=P and P2=P8Temperature=T1=T and T2=2TNow, P1T1n1=P2T2n2⟹PxM×T=P8n2×2T⟹n2=xM16∴(1−116)xg=15x16g of the gas escaped.

A vessel has $x$ $g$ of gas at high pressure $P$ . When certain gas escapes, the pressure $P$ became $P / 8$ and temperature $T$ became $2 T$ . What is the amount of gas escaped?