TBR physics II pg 38 help

[jchen08]

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Question 40 asks:

For lungs w/ a tidal volume of 400 mL and a total volume following normal expiration of 1200 mL, how does internal pressure change to cause inspiration?

Answer: b) it decreases by 25%

Can someone explain why it is not d) it decreases by 33%? I don't understand their solution. Thanks!

 

[MT Headed]

PV=nRT. They are modeling breathing as a process where your body changes V, which initially causes P to change. Then because there is a change in pressure between the lungs and the air, air moves (n changes) to equlibrate the pressures at this new volume.

So on inspiration the volume of air goes from 1200 to 1600. That's an increase by a factor of 4/3. What would happen to the pressure if you did this? The new pressure would have to be the old pressure multiplied by 3/4, if the volume increased by 4/3.

What's a other way of saying the new pressure is 3/4 of its old value (75% of its old value)? Decrease it by 25%.

 

[superman3]

I remember this question. so so so tricky. Basically, you have to remember that even though pressure and volume are inversely correlated, that doesn't mean that because the volume increases by 33%, the pressure must decrease by 33%. It seems counterintuitve, but the math just doesn't work out. Best approach to use for these problems is a fraction/decimal based approach, since percentage increase/decrease appears to be convoluted for this type of calculation. Major props to TBR for this particular question though, very, very tricky and nice solution by MTHeaded.