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Avogadro's Law & Gay Lussac's Law

A gas cylinde...

Question

A gas cylinder containing cooking gas can withstand a pressure of 14.9 atmospheres. The pressure gauge of the cylinder indicates that the pressure at $27^{\circ}$ C is 12 atmospheres. Due to sudden fire in the building, the temperature starts rising. The temperature at which the cylinder explodes is

A

200°C

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B

99.5°C

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C

67.3°C

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D

123.8°C

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Solution

The correct option is
D
99.5°C
Since the gas is confirmed in a cylinder, its volume will remain constant.
From the given data,
$p_{1} = 12 b a r$ , $P_{2} = 14.9 b a r$ , $T_{1} = 27 + 273 = 300 K$
$\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}$
$T_{2} = \frac{14.9 \times 300}{12} = 372.5 K = {99.5}^{\circ} C$

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