A scheme for finding the internal volume 
of a gas cylinder consists of the following steps. The cylinder is filled with a gas to a low pressure 
and connected through a small line and valve to an evacuated reference tank of known volume 
. The valve is opened, and gas flows through the line into the reference tank. After the system returns to its initial temperature, a sensitive pressure transducer provides a value for the pressure change ?P in the cylinder. Determine the cylinder volume 
class="w-image" /> from the following data:
What will be an ideal response?
? ?P / P 1 = ?0.0639
Before the valve is opened, when all of the gas is in cylinder B, at pressure 
we can write the number of moles of gas (assuming it to be ideal) as
After the gas is allowed to expand into the second tank and return to the initial temperature, we can write the total number of moles in terms of the final pressure 
+ ?P) and total volume 
as
Both the number of moles of gas and the temperature are the same before and after the expansion. So, we can write
Solving this for the unknown volume 
gives
Putting in the numbers, we have
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