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Chapter 3: Q65PP (page 645)

You have a cylinder that contains 500 L of the gas mixture pressurized to 2000 psi (gauge pressure). A regulator sets the gas flow to deliver 8.2 L>min at atmospheric pressure. Assume that this flow is slow enough that the expansion is isothermal and the gases remain mixed. How much time will it take to empty the cylinder? (a) 1 h; (b) 33 h; (c) 57 h; (d) 140 h.

Short Answer

Expert verified

Option (d) 140h is the correct answer

Step by step solution

01

Step 1:

In the isothermal expansion temperature is constant. use the ideal gas law,

pV = nRT

02

Step 2:

T,n and R are constant relation between initial and final state is,

p1V1=p2V2V2=V1p1p2

To calculate final volume flow rater=Vt where t is time that cylinder takes to empty

Thus,

V2=V1p1p2V2=500200014.8V2=67.567×103L

03

Step 3:

Time that cylinder takes to be empty

t=V2r

t=67.5678.2L/min×103Lt=8239mint=140h

Thus, the time taken by the cylinder to get empty is 140h

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