91Ó°ÊÓ

Work Done by the Lungs. The graph in Fig. E19.4 shows a pV-diagram of the air in a human lung when a person is inhaling and then exhaling a deep breath. Such graphs, obtained in clinical practice, are normally somewhat curved, but we have modelled one as a set of straight lines of the same general shape. (Important: The pressure shown is the gauge pressure, not the absolute pressure.) (a) How many joules of net work does this person’s lung do during one complete breath? (b) The process illustrated here is somewhat different from those we have been studying, because the pressure change is due to changes in the amount of gas in the lung, not to temperature changes. (Think of your own breathing. Your lungs do not expand because they’ve gotten hot.) If the temperature of the air in the lung remains a reasonable 20°C, what is the maximum number of moles in this person’s lung during a breath

Step by step solution

01

To calculate the work done by the person’s lungs.

We, know that the work done W is equal to the area under the curve. Therefore, to calculate the area under the curve, we will multiply the number of squares in the closed loop by the area of one square.

From the figure it is clear that the total number of squares = 74 .

Now, one square has a dimension of 1mmHg on p-axis, and dimension ofon V-axis. Therefore, the are of the square = 1mm Hg x 0.1mmHg.L

Now, Work done 0.059ml

Therefore, the work done by the persons lungs is 7.4mmHg.L

02

To Calculate the maximum number of moles

From Ideal gas law we know that

$n_{max}=\frac{P_{max}{V}_{max}}{RT}$

From the figure it is clear that$p_2=11mmHg$ , and volume$V_2=1.4L=1.4×{10}^{-3}{m}^3$ .

Now,

role="math" localid="1664297362401" $$\begin{gathered} P_{max}=p_2+p_{air}=11mgHg+760mmHg \\ =771mmHg \\ =1.028×{10}^{5}Pa \end{gathered}$$

Now substituting the values of$V_{max}$and$p_{max}$we get

$$\begin{gathered} n_{max}=p_{max}{V}_{max/RT{n}_{max}} \\ =1.028×{10}^{5}pax1.4×{10}^{-3}m3/8.314J/m.K×273K{n}_{max} \\ =0.059mol \end{gathered}$$

Therefore, the maximum number of moles in the lungs is

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