Ideal Gas Law: Question about a compressor exam question

  • #1

Homework Statement:

A compressor pumps 70 L of air into a 6 L tank with the temperature remaining unchanged. If all the air is originally at 1 atm, what is the final absolute pressure of the air in the tank?

a) 13.7 atm

b) 9.3 atm

c) 11.7 atm

d) 12.7 atm

e) 15.1 atm

Relevant Equations:

PV=nRT
This is a question in my midterm. I calculated for the answer as c) 11.7 atm by the Ideal Gas Law. The professor states that "all the air is originally at 1 atm" in the prompt indicates an idea of "both 70 L of air and existing 6 L of air in the tank are at 1 atm", and he grades d) 12.7 atm as the correct answer.
However, there is no clear statement to support that the tank is filled with air, and I think "all the air" should refer to the idea that "all compressed 70 L of air is uniformly at 1 atm at start". Also, I googled the same question and got all same answers as 11.7 atm. Here are the links:
https://www.prepdoor.com/engineerin...-into-a-6-l-tank-wit/59efcb100a975a0f1cd65996
https://doubtnut.com/question-answe...ure-remaining-unchanged-if-all-the-a-10965975
So, in a rigorous perspective, which one would be more correct? Is it c) 11.7 atm or d) 12.7 atm?
 

Answers and Replies

  • #2
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Obviously this comes down to an opinion about how to interpret the question. I would interpret it as your professor did. If the question had said, "The air is originally at 1 atm," then I would have interpreted it as you did. The reason is that by saying "all the air," I think the description is extended beyond just the mass pumped in, for it would be weird to think of 70 liters of air surrounding a compressor (a relatively small amount) as varying wildly in pressure especially in a idealized problem. However it would not be unusual for the air inside a tank that stores compressed air to be at a different pressure than the air surrounding it. The problem just as easily could have read "The air initially inside the tank is at 2 atm," or the like.

Is this question going to ruin your grade?
 
  • #3
berkeman
Mentor
57,718
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However, there is no clear statement to support that the tank is filled with air
You are right that the question is a little ambiguous, but the most common starting condition for a compressor tank is "empty", which means that its relief valve has been opened to let pressure escape, and then closed after the pressure is relieved. This leaves the remaining air in the tank at 1atm.
The problem just as easily could have read "The air initially inside the tank is at 2 atm," or the like.
Yeah, it's also possible to start with a non-empty tank, in which case the pressure will be >1atm. But if that were the case that the problem wanted to refer to, I agree that it would have to have explicitly stated that.
 
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  • #4
Is this question going to ruin your grade?
Yes, if I got this correct, it will be easier to get an A for this course; otherwise I have to get 100% in the final. This question is really important to me.
 
  • #5
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For what it's worth, I interpreted this as 70 L of air at 1 atm being pumped into a 6 L tank initially containing air, also at 1 atm. The answer I got was 12.7 atm.
 
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