Air In Lungs - Thermal Physics

[ducksmad]

Homework Statement

A submarine has run into trouble and is stuck at the bottom of the ocean. Several people are on board and must make their way to the surface without any diving gear. The air pressure aboard the submarine is 3.36 atm. the air temperature inside the submarine is 18.51 C and you can take the body temp (inside the lungs) to be 36.38 C.

Homework Equations

A) 1)The first person to leave takes a breath as deep as possible by exhaling as far as possible leaving 1.03 L in their lungs then slowly inhaling to increase their lung volume by 4.98L
If the air temp in submarine was 18.51 C what volume of air is inhaled from surrounding?

2)The person unwisely holds their breath all the way up tp the surface. What would the volume of their lungs be?

B) The 2nd person to leave also takes a breath as deep as possible by exhaling to 1.06L of air left in the lungs and then slowly inhaling to increase their lung volume by 4.92 L, same body temp as above 36.38 C

How many particle of air do their lungs contain after inhaling?

The person breaths out all the way to the surface in order to maintain constant lung volume.How many moles of gas remain in lungs?

C)Given that the molar mass of C02 is 44.0 g/mol what is the root mean square velocity of a C02 molecule in the lungs?

The Attempt at a Solution

A)
1) I used V=Beta * temp change * initial volume

V = 0.0034 * (273+(36.38-18.51))*1.03
V=1.0186 L
The answer is suppose to be 4.69 L i have tried other formulas like the ideal gas law but cannot come to the same answer


Havent attempted the other questions as i don't know where to start
Would appretaite some help please on what to look at, have looked in a couple of textbooks and searched the net with no luck
Thank you in advance for any help that can be given

 

[Novaris]

Hey ducksmad. Sounds a little like physics 160 there..

but anyway.

for A-1). just use PV = nRT. the question suggests constant pressure. So Charles law applies?

$$\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}$$

Um... so .

Let $${V_{1}}$$ = volume of the lung (4.98L)
Let $${T_{1}}$$ = temperature of the body (309.38K)
Let $${T_{2}}$$ = temperature of the submarine (291.51K)
Let $${V_{2}}$$ = be your unknown

substitute, rearrange and calculate as necessary, and you should get 4.69 to 3 s.f.

The others, I am not so sure.

For A-2) I assumed that temperature was constant, and that the surface pressure was 1 atm.

Hence, $${P_{1}}{V_{1}} = {P_{2}}{V_{2}}$$

For this one, $${V_{1}}$$ is the sum of the initial and the change in volume.

Other questions.. still being worked out.

Meanwhile, I'd also appreciate an explanation as to why the total lung volume was used rather than the change in volume. //edit: volume used is the change, misread question, which says increased "by" xx L. not "to" xx L

Thanks.

PS. love how the forum supports LaTeX

 

[tomcue]

Hello,

I would like to provide some insights and guidance on how to approach this problem.

Firstly, let's start by understanding the concept of air pressure and its relation to volume. According to Boyle's Law, the pressure and volume of a gas are inversely proportional at a constant temperature. This means that when the pressure increases, the volume decreases and vice versa.

In the given scenario, the air pressure inside the submarine is higher than the atmospheric pressure at the surface. This means that the volume of air inside the lungs will decrease as the person ascends to the surface. However, the body temperature will remain constant as it is regulated by the body's internal mechanism.

Now, let's look at the equations provided in the homework statement.

A) 1) The first question asks for the volume of air inhaled from the surrounding when the person takes a deep breath and increases their lung volume by 4.98 L. To solve this, we can use the combined gas law, which takes into account changes in pressure, volume, and temperature. The equation is as follows:

(P1V1)/T1 = (P2V2)/T2

Where P1, V1, and T1 represent the initial pressure, volume, and temperature, respectively, and P2, V2, and T2 represent the final values after the change. We know that the pressure, temperature, and initial volume are given, and we need to find the final volume. Rearranging the equation, we get:

V2 = (P1V1T2)/(T1P2)

Substituting the values, we get:

V2 = (3.36*1.03*291.38)/(273*1)

V2 = 4.69 L

This is the same answer as provided in the homework statement.

2) The second question asks for the volume of the person's lungs when they hold their breath all the way to the surface. This can be calculated by using the ideal gas law, which relates the volume, pressure, and number of moles of a gas at a given temperature. The equation is as follows:

PV = nRT

Where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. We know that the pressure and temperature remain constant, and we need to find the volume. Rearranging