The volume of a large irregularly shaped tank is determined as follows. The tank is first evacuated, and then it is connected to a 50 L cylinder of compressed helium gas. The gas pressure in the cylinder, originally at 21 atm, falls to 7.0 atm without a change in temperature. What is the volume of the tank?

100L

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150L

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200L

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300L

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Solution

The correct option is A 100L
$P_{1} \times V_{1} = P_{2} \times V_{2}$
$P_{1} = 21 a t m =$ initial pressure of 50 L cylinder
$P_{2} = 7.0 a t m =$ final pressure of 50 L cylinder and tank
$V_{1} = 50 L =$ volume of cylinder
$V_{2} =$ volume of cylinder and tank
$21 a t m \times 50 L = 7.0 a t m \times (50 + V) L$
$(50 + V) L = 150 L$
$V = 150 - 50$
$V = 100 L$
The volume of the tank is 100 L.

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