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Liquefied natural gas (LNG) is mainly methane. A $10 m^{3}$ tank is constructed to store LNG at $- 164^{0} C$ and 1 atm pressure, under this condition density of LNG is $415 kg / m^{3} .$ The volume of storage tank capable of holding …. mass of LNG as a gas at $20^{0} C$ and 1 atm pressure will be

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$1250 m^{3}$

$5280 m^{3}$

$6230 m^{3}$

$9870 m^{3}$

answer is C.

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Detailed Solution

$mass of {CH}_{4} in cylinder = V \times d = 10 \times 415 \times 1000 g; n = \frac{10 \times 415 \times 1000}{16} = 2 .59 \times 10^{5}$

At $20 ° c and 1 atm,$

$\begin{array}{l} V = \frac{nRT}{P} = \frac{2 .59 \times 10^{5} \times 0 .0821 \times 293}{1} \\ = 6 .23 \times 10^{6} L = 6230 m^{3} \end{array}$

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