Troubleshooting Air Volume Increase: -3.5°C to 37°C

[mikep]

can someone please help me with this problem?
After emptying her lungs, a person inhales 4.5 L of air at -3.5°C and holds her breath. How much does the volume of the air increase as it warms to her body temperature of 37°C?
i used the equation $$\displaystyle{\frac{V}{T}} = \displaystyle{\frac{V}{T}}$$

$$\displaystyle{\frac{4.5L}{269.5K}} = \displaystyle{\frac{V}{310K}}$$ V = 5.18
but i got the wrong answer. can someone please tell me what I'm foing wrong?

 

[Sirus]

You found the final volume. What is the question asking for...?

I think you'll see it.

 

[mikep]

oh ok i tried 5.2 - 4.5 = 0.7 but i still got it wrong

 

[Sirus]

Ha! The question fooled us both. Upon re-reading, I realized that the volume will not increase because she is holding her breath. Pressure will increase.

Good fun.

 

[mikep]

wouldn't the pressure decrease? i tried 0 as an answer but it didn't work

 

[cAm]

wouldn't the pressure decrease? i tried 0 as an answer but it didn't work

No... the pressure Would increase because the volume tries to increase as temp increases, but the lungs confine it to the same volume...

 

[mikep]

so is the answer suppose to be 0?

 

[cAm]

as far as i can tell...

but i could easily be wrong... =/

 

[Physics is Phun]

well the question doesn't say that she fills her lungs. it just says she empties them and then breathes in 4.5 litres so I don't think you can assume her lungs are filled at this point. Unless you've been studing average lungcapacity or the pressure lungs exert on air then I think what you did in the first and third posts would be correct.

 

[Sirus]

I don't think so. Remember that no matter how little air she takes in, it will spread to occupy the entire volume of her lungs because it is in gaseous phase. Once that happens, any increase in temperature will cause an increase in pressure according to:
$$PV=nRT$$
When volume (V), amount of gas (n), and the constant (R), are constant, $P~\alpha~T$.

I think the answer should be 0.