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Standard X

Physics

Ideal Gas Equation

Air is filled...

Question

Air is filled in a bottle at atmospheric pressure and it is corked at $35^{o}$ C. If the cork can come out at $3$ atmospheric pressure, the upto what temperature should the bottle be heated in order to remove the cork.

{325.5}^{o}

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851^{o}

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651^{o}

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None of these

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Solution

The correct option is C $651^{o}$ C
We know that $ρ_{1} V = n R T_{1}$
$\Rightarrow 1 \times V = n R (35 + 273)$
$= n R \times 308$ ............(i)
and $ρ_{2} V = n R T_{2}$
$\Rightarrow 3 \times V = n R T_{2}$ ............(ii)
On dividing Eq. (ii) by Eq. (i), we get
$3 = T_{2} / 308$
$\Rightarrow T_{2} = 924$ K
$T_{2} = 924 - 273$
$= 651^{o}$ C.

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Air is filled in a bottle at atmospheric pressure and it is corked at 35oC. If the cork can come out at 3 atmospheric pressure, the upto what temperature should the bottle be heated in order to remove the cork.

The correct option is C 651oCWe know that ρ1V=nRT1⇒1×V=nR(35+273)=nR×308 ............(i)and ρ2V=nRT2⇒3×V=nRT2 ............(ii)On dividing Eq. (ii) by Eq. (i), we get3=T2/308⇒T2=924KT2=924−273=651oC.

Air is filled in a bottle at atmospheric pressure and it is corked at $35^{o}$ C. If the cork can come out at $3$ atmospheric pressure, the upto what temperature should the bottle be heated in order to remove the cork.